What Cat Con do i need?

Hey guys i need a new catalytic. Seems mine is plugged. Now ive got an s13, with a bings 3" cat back. Will the direct fit OE replacement cat with flanges still be a direct fit? I know its not ideal to go OE, and the hi flows seem to be cheaper but its the only one i can get on short notice without having to drive anywhere. But i dont understand how the pipe can go from 2" pre cat and 3" post cat. Is it the way s13 cat backs are flanged? So they all mate up with the oe catcon? Im pretty sure im on the right track with this idea, because all cat back how to’s rarely mention anything about changing the cat. Just want to verify before i drop $135. Thanks

edit I just ordered the oe direct fit cat from bosal exhaust. Had to get it today and the deadline was 10 am to get it today. I’ll let you guys know how I make out.