Is free trade transitive? If country A has a free trade agreement with country B, and country B has a free trade agreement with country C, does that mean country A effectively has a free trade agreement with country C?

If the answer is “it depends what you mean by free trade”, what characteristics of the A-to-B agreement would be be conducive to it being “transitive” with the B-to-C agreement?

If A-to-B and B-to-C were perfectly “compatible” in this sense, could A ship goods directly to C or would they still have to go via B?
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.