Actually I have a this doubt about this conflict serializability as stated in the question. I do know that we try to swap non conflicting insturctions in a scheudle of different transactions (not the same one as sequential order of transaction must be preserved).
For my doubt I observed that with conflicting pair of instructions of different transactions can form a dependency on each another as which instruction should be executed first which is why this schedule won't be equivalent to serial schedule.
That's my take on it please add more info or let me know what should be the right answer for it.