For a rational homology 3-sphere Y with a Spin c structure s, we show that simple algebraic manipulations of our construction of equivariant Seiberg-Witten Floer homology in [5] lead to a collection of variants HF SW,− ) which are topological invariants. We establish a long exact sequence relating HF SW,± * ,U(1) (Y, s) and HF SW,∞ * ,U(1) (Y, s). We show they satisfy a duality under orientation reversal, and we explain their relation to the equivariant Seiberg-Witten Floer (co)homologies

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... uced in [5]. We conjecture the equivalence of these versions of equivariant Seiberg-Witten Floer homology with the Heegaard Floer invariants introduced by Ozsváth and Szabó.