Lets assume that Britain for whatever reason opts out of the war in 1940-41 (Halifax, worse BOB, Better Italian performance and threat against the Empire etc) AND Barbarossa starts out well for the Germans despite the lack of surprise.
Would it be possible for the Axis to pursuade Turkey to join in (say in August/September 1941)?
What would Turkey like to gain?
What could they contribute? Could they put any real real pressure on the Russian Southern front?
If naval supremacy could be established in the Black sea, what would be the axis benefits? I assume an easier fall of Sevastopol, later shipments in via Rostov. How about Novorossijsk and Sochi? Could they be used to alleviate supply line stress or is the connecting infrastructure to poor?