Hello Thierno
There are two situations where the re-convergence takes place. The first is in the case of the lesson, where when port fa0/14 is shutdown, there is a complete carrier loss. In this case, the port with the best BPDU information is immediately invalidated. This means that the next best port is immediately chosen, which is fa0/16 without delay, so no 20 seconds are wasted in blocked mode. This is why the transition took 30 seconds, 15 in listening and 15 in learning.
Now if there were another switch between SW1 and SW3, and that switches connection to SW1 failed, fa0/14 would still be active, so no immediate loss of connectivity would be detected by SW3. This means that the whole BPDU exchange process would have to inform SW3 that more valid BPDUs are being received now from fa0/16, so it would then transition using the blocked>listening>learning procedure of 50 seconds.
I hope this has been helpful!
Laz