Horizontal Heegaard splittings of Seifert fibered spaces

We show that if an orientable Seifert fibered space M with an orientable genus g base space admits a strongly irreducible horizontal Heegaard splitting, then there is a one-to-one correspondence between isotopy classes of strongly irreducible horizontal Heegaard splittings and elements of ‫ޚ‬ 2g .This correspondence is determined by the slopes of intersection of each Heegaard splitting with a set of 2g incompressible tori in M. We also show there are Seifert fibered spaces with infinitely many nonisotopic Heegaard splittings that determine Nielsen equivalent generating systems for the fundamental group of M.