Constructing a Walsh diagram of AH2 According to Wikipedia, for the $\ce{AH2}$ Walsh diagram:



and the Walsh diagram in Shriver and Atkins Inorganic Chemistry, the $a_1$ orbital sinks in energy going from 90 to 180°. Furthermore, the $b_2$ orbital at 90° is higher in energy than the $a_1$ (lone pair).

However according to the second, newer diagram for a AH2 molecule on the same page:



the $a_1$ is rises in energy and the $b_2$ is definitely lower in energy than  the $a_2$ (or $a_1$ lone pair). This matches also my own self-made diagram, using Hartree-Fock 6-31G*, calculated through Spartan. Other pages use the same Walsh diagram.

What is going on here? 

Shrivers textbook explains the rise of the $a_1$ orbital through decreased H-H overlap and reduced involvement of the $\ce{X~2_{pz}}$.
I'd say the diagram from Atkins "Inorganic Chemistry" is in error.

I went to what I consider the "definitive source" for such Walsh diagrams: Orbital Interactions in Chemistry by Albright, Burdett and Whangbo.

Here's their diagram for $\ce{H2S}$ (the linear on the left, the bent on the right):



They don't readily indicate the method they used for the calculation, but on this energy scale the difference between the $1\sigma_g$ and $1a_1$ is minimal. They show that the $1a_1$ is lower in energy since the interaction with the central p orbital will be stabilizing.

As to the $1b_2$ rising above the $2a_1$ in the bent structure -- the diagram from Albright, Burdett, and Whangbo agree that there's no "crossing."