What filters Lee?
If transistors had infinite GBW product and no Ft effects, then it would be much easier to design ideal amplifiers and tailor the characteristics by applying appropriate filters. Unfortunately DC to daylight amplifiers are not possible. The inherent filter effects of transistors (the Ft parameter) get in the way.
For example, the long tailed pair formed by Q1 and Q2 (take out any of the capacitors in that circuit) has a lot of gain at low frequencies but hits a point at the Ft frequency where its gain tails off at 6dB per octave (single pole). Each succeeding transistor in the amp has its own similar characteristics at different frequencies. These all contribute to a multi pole behavior that has to be compensated for. That is what most of the capacitors in the circuit are attempting to do, kill the gain in a determistic manner before the effects of these transistor poles start contributing.