  Given a three-manifold with b_1=1 and a nontorsion spin^c structure, we use
finite dimensional approximation to construct from the Seiberg-Witten equations
two invariants in the form of a periodic pro-spectra. Various functors applied
to these invariants give different flavors of Seiberg-Witten Floer homology. We
also construct stable homotopy versions of the relative Seiberg-Witten
invariants for certain four-manifolds with boundary.
