Abstract
A Haken sphere S in a 3-manifold M with a Heegaard splitting V∪ F W is a separating 2-sphere in M which intersects the Heegaard surface F only in an essential circle in F. It is known how any two Haken spheres in the genus 2 Heegaard splitting of S 3 or a connected sum of two lens spaces are related. In the present paper, we show how any two Haken spheres in a genus 2 Heegaard splitting of S 2×S 1 # S 2×S 1 or S 2×S 1 # L(p,q) are related, where L( p, q) is a lens space.
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