"The tango with Turkey has its limits", says retired Israeli Colonel Dr. Eran Lerman, Vice President of the Institute for Strategy and Security in Jerusalem.
The first Israeli foreign minister to visit Greece since the inauguration of Kyriakos Mitsotakis' new government was Israel's Eli Cohen, a sign that both countries see the importance of their relationship and the new alignment of forces in the Eastern Mediterranean.
While new avenues for dialogue between Jerusalem and Ankara are opening up - including a planned visit by Prime Minister Benjamin Netanyahu, officially confirmed by Erdogan - Israel's priorities should remain firm.
We must vigorously resist pressure for a deal on a gas pipeline to Turkey.
In terms of national security, cooperation with Greece and Cyprus is a game changer, giving Israel vital strategic depth during a conflict.
Hence the importance of working with both of these countries, but also of supporting Cyprus' freedom to make its own foreign policy decisions.
The convincing victory of Kyriakos Mitsotakis' centre-right New Democracy (ND, New Republic) party in the second round of the Greek parliamentary elections on 25 June stabilises the political scene in Athens.
ND now has an absolute majority with 158 out of 300 MPs in parliament. In fact, a cycle of elections in Eastern Mediterranean countries has been completed, confirming the presence of experienced political personalities in power.
All this while Benjamin Netanyahu has been ruling Israel since 29 December with a stable parliamentary coalition (despite the considerable turmoil over judicial reform).
Nikos Christodoulides, former foreign minister, was sworn in as president of Cyprus on 28 February.
Recep Tayyip Erdogan, who won the second round of Turkey's presidential election (28 May) and was sworn in for a third term (3 June).
This means that "experienced politicians" are in charge throughout the region, with the ability to plan (in Egypt, Al Sisi continues to rule).
This, in turn, can create opportunities to strengthen existing ties of cooperation, and explore new options for resolving or reducing old conflicts.
In this context, the visit of Israeli Foreign Minister Eli Cohen (6 July),the first of its kind hosted by Greece's new Foreign Minister George Gerapetritis, marked the importance both countries attach to their cooperation and their role in the Eastern Mediterranean region.
The common perceptions of threats and opportunities, the affinity of values and the prospect of economic cooperation, especially but not exclusively in the energy sector, are all part of this new "bridge in the Mediterranean".
Israel is extensively involved in strengthening Greek military capabilities.
The Israelis have become an important part of Greece's tourist trade and major investors in Cyprus. Israel strongly supports the position of Greece and Egypt on the delineation of the EEZ in the Eastern Mediterranean, in contrast to the lines drawn by Turkey and the Government of National Accord in Tripoli.
Ultimately, Greece is likely to become, if not a hub more likely, a Mediterranean energy pipeline to Europe.
Meanwhile, Israel should be able to reassure Greece and Cyprus that there will be no accommodation with Erdogan, which is against their interests.
What should be Netanyahu's agenda in Turkey?
The repeated hints and pressures used by Erdogan and his government to persuade Israel to export gas from Mediterranean deposits through Turkey (helping it to establish itself as an energy hub) are ultimately pointless.
Such a project would immediately conflict over the use of the Cyprus Exclusive Economic Zone.
Israel does not wish to be tied to an Islamist leadership in Turkey, which still harbours hostile feelings and may turn radically against Israel in times of crisis, particularly in a confrontation with Hamas.
So what should be on the agenda during Netanyahu's visit to Ankara if he rejects (however politely) Erdogan's push for a pipeline to Turkey?
There are, as it happens, significant other areas in which the two countries,despite bitter differences in the recent past, that the two countries can find common ground, even if Israel shies away from such a commitment and refuses to swap its strategic cooperation with Greece and Cyprus.
The scope of trade, clearly in Turkey's favour, continues to increase and may increase even more (albeit marginally) if the present Israeli government goes ahead with its plans to reduce the cost of living by allowing imports of agricultural products.
The poor performance of the Turkish economy in recent years has in some places seemed to call into question Erdogan's political survival.
Better relations with Israel, as well as with the United Arab Emirates and Saudi Arabia, can help free Turkey from its current predicament.
Finally, on the issue of the Mediterranean theatre, Israel, Greece and Cyprus have taken a differentiated position, which leaves the doors of the gas "club" open to all those who can prove to be "like-minded".
Erdogan's neo-Ottomanism of the past decade does not fit into this effort, since he claims half of the Aegean in the name of "Mavi Vatan", the doctrine of the "Blue Homeland".
If Erdogan is willing to distance himself from such fantasies, Israel could help chart a course towards greater regional integration (which may also reflect Turkey's position in Washington), but not at the expense of what has already been achieved.
These oblige Israel to firmly support the Greek-Egyptian position on EEZ delimitation, in contrast to the one being taken by Turkey and the "Government of National Accord" in Western Libya.
Turkey need not be left out: the growing LNG/FLNG capacity could also provide gas (Israeli, Egyptian or Cypriot) sent to Turkish liquefaction facilities, but this would ensure flexibility rather than a rigid mutual dependence.
The importance of Cyprus for Israel's strategic depth One of the key reasons for Israel's need to maintain and expand its trilateral relations with Greece and Cyprus has to do with the potential role that they may be asked to play if Israel becomes involved in a total confrontation in the North (as it increasingly seems.
Possibly, given Hezbollah's recent provocations), possibly including in Gaza. Given the range of Hezbollah's missiles and rockets, Israel's ports and airports may face a degree of threat that foreign commercial operators will not accept.
In such a scenario, national carriers, such as El Al Airlines and Zim Shipping, in which the Israeli government has a decisive stake that allows it to use them in an emergency, would have to support the national lifeline: and the nearest logistical 'base' from which they could do so would be Cyprus and Greece.
Interestingly, references to "strategic depth" emerged in comments made by senior Cypriot officials and officers at the latest round of the Israel-Greece Forum, organised by the Cyprus Centre for European and International Affairs in cooperation with B'nai B'rith.
It is a potential aspect, already reinforced by the large-scale military exercises conducted by the Israeli army in Troodos on an annual basis, that makes it important for Israel to support Cyprus' continued ability to implement its own foreign policy and national security options without a veto from Ankara.
Even if there were to be renewed progress towards an agreed permanent status on the island as a whole - which Israel and all others in the Eastern Mediterranean should warmly welcome - this requirement to maintain independent decision-making, vital to all parties, must be respected, he said.
