in the state diagram of APB, the master moves from one state to other state depending on the "transfer" is asserted or not, from which signal can I know the transfer is going to happen, is it from "PSELx"?
The answer will depend on the perspective of the APB component you are looking at.
If you are looking at the APB bridge from a more complex system bus like AXI or AHB, when that system bus tries to initiate a transfer to or from the APB, the "Transfer/No transfer" indication would be signalled by that system bus.
So for example if you were looking at an AHB to APB bridge, "Transfer" would be signalled by HTRANS[1]=1 (a NONSEQ or SEQ), HSEL=1 to this bridge, and HREADY=1. "No transfer" would be indicated by any other combination of those signals.
PSEL would then be determined by the state the state diagram moves into, so as a result of "Transfer/No transfer".
But if you are looking at the APB peripheral responding to requests, it will look at PSEL, PENABLE and PREADY to determine which operating state it is in, so then PSEL would indicate a transfer in operation.