Well i have to say i have seen a bunch of amvs which are fantastic. but in my opinion, this amv has got to be the best of all time. If you like Cowboy Bebop than this video surely will keep you enjoyed. The music is from Weezer and called "only in dreams." I know it probably has been up all over the internet and you have probably already seen it but i really like it i feel like watching the show again

Cowboy Bebop - Only In Dreams Youtube video