  For a rational homology 3-sphere $Y$ with a $\spinc$ structure $\s$, we show
that simple algebraic manipulations of our construction of equivariant
Seiberg-Witten Floer homology lead to a collection of variants which are
topological invariants. We establish exact sequences relating them, we show
that they satisfy a duality under orientation reversal, and we explain their
relation to ou previous construction of equivariant Seiberg-Witten Floer
(co)homologies. We conjecture the equivalence of these versions of equivariant
Seiberg-Witten Floer homology with the Heegaard Floer invariants introduced by
Ozsv\'ath and Szab\'o.
