The pure consciousness underlies all three states. The richest experience that we feel is the waking stage. It's very hard for us to will ourselves to deep sleep or somebody else to push us into it. What states want to and feel which we describe is unreal, but very real for us.
Swami Sarvapriyananda teaches one of the shortest and most profound upanishads accompanied by Gaudapada's Karika. This lecture covers Mantra 5-6.