  We construct a finite dimensional Kaehler manifold with a holomorphic,
symplectic circle action whose symplectic reduced spaces may be identified with
the tau-vortex moduli spaces (or tau-stable pairs). The Morse theory of the
circle action induces natural birational maps between the reduced spaces for
different values of tau which in the case of rank two bundles can be
canonically resolved in a sequence of blow-ups and blow-downs.
