In 1972 Richard Nixon repeals the Cuban Embargo Act and allows the same sort of trade with Cuba as with the countries of Eastern Europe.
How long before communism in Cuba collapses?
I'm not at all sure communism would really "collapse." You could see a sort of China-situation developing in Cuba, though obviously not on such a grand scale. The country's pumped full of foreign capital because they can make things cheaper and because the (probably) booming rebirth of the tourism and gambling industries could make the island quite wealthy.
So, like China now, communism doesn't "collapse," but rather just becomes an ideology that takes backseat to budding corporatism.
China is the largest and most populous country on Earth, Cuba is a smallish island near an economic hyperpower. I'd really expect Cuba to react more like Poland or East Germany too an open door policy from the USA.
Except Cuba is nothing like a Soviet puppet like E Germany. Its revolution was homegrown, and it's proven it can survive the fall of the Soviets by several decades.