Abstract
In this paper we deal with all 3-manifolds which are obtained by glueing the boundaries of two Seifert fibered spaces over a disk with two exceptional fibers. We will give a necessary and sufficient condition for those 3-manifolds to admit Heegaard splittings of genus two. Moreover we will evaluate the numbers of Heegaard splittings of genus two, up to isotopy, of those 3-manifolds. In fact, we will see that the numbers are at most four.
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