ISTANBUL—Turkey and Israel’s political divergence in the past few years is of little concern to businessmen, especially when some of the world’s largest natural gas deposits are at stake. Israel, together with Cyprus, sits on more than 120 trillion cubic feet of natural gas in the Eastern Mediterranean, according to U.S. Geological Survey assessments. That’s enough to meet natural gas needs for 2,400 years in energy-starved Turkey, which relies on Russia for 60% and Iran for 20% of its imports. The trick is navigating the choppy political waters. It’s a difficult proposition as Turkey-Israel ties have been at best strained for the past three years, and Ankara doesn’t even recognize the Cypriot government in Nicosia. But executives from Turkish and Israeli energy firms say their deals can allow corporations to surmount the obstacles politicians can’t overcome. If they succeed, Turkey may see a fifth of its annual natural gas […]