Aw man, this is basically what my thread is about. As a fellow Aeon Crusader, I find the Mantis particularly frustrating as well. If I play a match before going to bed I can hear the Mantis' lasers in my head when I close my eyes
The only thing you can really do is move your tanks back when they rush you, but they will catch up with you quite quickly. And this micro is all well and good, but you can't be everywhere at the same time. There seems to be a thing with Manti as well, I notice that I always seem to be on the back foot against a Cybran player as they always have more Manti than I have tanks. It's as though the Manti build time is 10 seconds instead of 13, but I know it's 13 seconds but it seems shorter. Another thing with Manti is that they build up a critical mass very quickly due to their speed, in the early game all the Cybran player has to do is press control+Z and then because the Manti are so fast they will group together into a big swarm very early on. I think the answer as an Aeon is to play a more defensive game and focus on defending your expansions instead of trying to destroy the enemy's expansions and then gradually push the enemy back as you expand more and more.