Unstable pseudo-isotopies of spherical 3-manifolds

In our previous works, we constructed diffeomorphisms of compact 4-manifolds $X$ by surgeries on theta-graphs embedded in $X$. In this paper, we consider the case $X=M\times I$, where $M$ is a spherical 3-manifold. For some of such $X$, we compute lower bounds of the ranks of the abelian groups $\pi_0\mathrm{Diff}(X,\partial)$. We study the behavior of the elements constructed by theta-graph surgery under the suspension functor in stable pseudo-isotopy theory, and their triviality in the space of block diffeomorphisms.