Studying the Hubble's Galactic Classification Scheme
Why are there not more active galaxies in our area?
If you mean Local Group of galaxies by saying "our area", they are galaxies with low red shifts. We observe them on late stages of cosmological development when their energy resources have been spent (relatively) over the course of evolution. Galaxies with very high red shifts are considered to be younger because they point to early stages of the Universe (up to ten billions light yesrs away from here. Ten bilions years is a time interval needed for the light to travel that distance ). Those galaxies haven't spent yet much of their initial energy. Keep in mind: the deeper we go into the space the younger objects the (earlier stages of the Universe) we observe. Young objects are always dsitinguished by their activities, explosions, etc.