Consider the Large and small signal model of the MOSFET amplifier,

^{simulate this circuit – Schematic created using CircuitLab}

How is this transformation valid, I get the linearization of the MOSFET, but then how can a source become a short and how can we reason the simplifications of other elements. I mean, the original circuit looks totally different from the small signal model. Please provide an intuitive answer, as I get the math part (i.e.) for small signal variations, the behavior of various elements are studied and then approximated, My question is how is this valid?