-Analysis- BEIRUT — The Al Udeid Air Base in Qatar is one of the facilities that the U.S. is using to supply the Israeli military with weapons and ammunition for its war on Gaza. The Israeli daily Haaretz has documented dozens of U.S. military transport planes traveling from Al-Udeid to Israeli military airports. Yet Doha is also Hamas’s alternative capital, where the group’s exiled leadership resides. And it is from the Qatari capital that Hamas’s military wing, the Qassam Brigades, broadcast — via Al Jazeera — its first statement on the the Oct. 7 attack. For the latest news & views from eve…