Pegasus as the flying horse Belepheron rode
Hi Geoff,
Yes, I read a simple version of the story of Bellerophon to my son fairly recently. I believe Bellerophon wanted to take on the Chimera (3 different heads, all breathing flame ), which was terrorising his land. Being a strategist well ahead of his time, he thought that the Chimera could be beaten from the air, i.e. with the aid of Pegasus.
In this version of the story, he managed to break Pegasus (assisted by a special bridle), but then took pity on the magnificent animal, so set it free, deciding he must find another way to beat the Chimera. Pegasus (of course) returns to him, deciding to help of his own free will. By implication, had he not done so, the Chimera would have won in the battle that ensued, as Pegasus has a fairly hard time of it.

I was a little confused as to where Perseus came into the equation, probably because one of those wonderful Ray Harryhausen (movie) re-tellings of the Perseus myth had Perseus taming Pegasus. But having checked it up using the wonderful site below:
http://www.pantheon.org/articles/p/pegasus.html
the Perseus story came first. Pegasus was the offspring of Poseidon and Medusa, possibly created by Medusa's head being dropped into the sea.

I love the way myths work, and that there is a sense of natural order in something wonderful emerging from something unspeakably repellent.

How is Pegasus linked to the muses, thus to poetry?
Well, quite apart from WW's comprehensive Pegasus-Muses link below, Pegasus clearly stands for imagination. Imagination is often depicted as a pair of wings (flights of imagination or airy fairy nonsense?). Attaching those wings to a fast horse, which would in any case give the sensation of flight, sort of doubles the effect. And, of course, Pegasus is usually depicted as a white horse, which is itself a creature of the imagination (I think ).

In a way the foul beasts (tyrants, those who rule by might and fear) are beaten by creative thinking. However, there's always a sting in the tail (or a gadfly on the arse) in that when the heroes start crediting themselves, rather than their gifts, they suffer and often die. Good ol' hubris.

Fisk