  The Vafa-Witten equations (with or without a mass term) constitute a
non-linear, first order system of differential equations on a given oriented,
compact, Riemannian 4-manifold. Because these are the variational equations of
a functional, the linearized equations at any given solution can be used to
define an elliptic, first order, self-adjoint differential operator. The
purpose of this article is to give bounds (upper and lower) for the spectral
flow between respective versions of this operator that are defined by the
elements in diverging sequences of reducible solutions. (The spectral flow is
formally the difference between the respective Morse indices of the solutions
when they are viewed as critical points of the functional.) In some cases, the
absolute value of the spectral flow is bounded along the sequence, whereas in
others it diverges. This is a curious state of affairs. In any event, the
analysis introduces localization and excision techniques to calculate spectral
flow which may be of independent interest.
