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Both Turkey and Israel are ardent opponents of Syria and the Shiite-Iranian factor in the region. The aggravation of relations between Turkey and Iran pushed Ankara into an alliance with Israel.
Both Turkey and Israel are not interested in the real reunification of their Syrian neighbor. The Turks want to control the north of the country, inhabited by Turkmen, buy cheap oil from ISIS, and occupy the bases of the Kurdish militias that threaten Turkey. Israel wants to eliminate the base of support for Hezbollah and one of its most dangerous enemies in the region. For this it is necessary that Syria remains a conglomeration of mutually hostile groups, or to break it up into several smaller states.
In addition, Israel is illegally occupying the Syrian Golan Heights, where significant deposits of oil were previously found, and is not ready to give them back to Syria.
Both countries are allies of the United States and opponents of the continental union of Russia and Iran. The Turkish-Israeli alliance was the pillar of American strength in the Eastern Mediterranean during the Cold War. Now the US is recovering lost ground.
Turkey intends to end its dependence on Russian gas. One alternative gas supplier may be Israel. Deliveries could begin in 2019.
If the Turks are buying oil from ISIS, Israel buys this oil from the Turks. Given that Israel is bombing only those who fight against ISIS, it is not hard to see whom the Zionist state actually helps in the present war. It is obvious that despite the rhetoric of both countries, they do not really perceive ISIS as a serious threat to them.
Most of all, the formation of the Ankara-Tel Aviv axis is a win for the US and Israel. By transforming Turkey into its ally, Israel undermines support for the Palestinian resistance, which previously lost the support of Syria when the civil war in the country broke out. The US reinforces the anti-Syrian coalition, including Israel into one unit with Saudi Arabia, and even the implacable enemy of the Jewish state - Qatar.