Is free trade transitive?
Free trade agreements are not transitive. Each country in a free trade agreement needs to ratify it with a legislative or regulatory body. Otherwise there is no legal basis for it to function and customs officials won't be able to observe it.

In practice if A and B have a free trade agreements and B and C do too, businesses can transship in the best case scenario. Or, most likely, ship from A to B, unload-unpack-repack-load using an intermediary company in B, and ship from B to C. That might cost less or more than paying import/export tariffs from A to C.