Fundamentally any good amplifier has no sonic signature. When combined with cables and a speaker the amplifier interacts through the cables and with the speaker such that the three create a unique sonic signature. There are three variables you have to consider to get a sound that you are now attributing just to the amplifier.
Amplifier technologies (design typologies) that have a propensity to create curtain definable types of signatures on average but each combination is again, unique. There are enough 'outliers' to this state that it is a general rule and not a law.
An equalizer, regardless of controls will shape the frequency and phase response of the above combination handling only the tonal aspect of the audio image you wish to create. Basic common use is to accommodate specific room-induced interaction with the speaker. Given that the whole system, that is the room, speakers, cables, and amplifier is a dynamic interactive 'thing', in the end we are lucky to get the sound we do.