  In this article, we study several closely related invariants associated to
Dirac operators on odd-dimensional manifolds with boundary with an action of
the compact group $H$ of isometries. In particular, the equality between
equivariant winding numbers, equivariant spectral flow, and equivariant Maslov
indices is established. We also study equivariant $\eta$-invariants which play
a fundamental role in the equivariant analog of Getzler's spectral flow
formula. As a consequence, we establish a relation between equivariant
$\eta$-invariants and equivariant Maslov triple indices in the splitting of
manifolds.
