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Following an example discovered by John Berge, we show that there is a4-component link L \subset (S^1 x S^2)#(S^1 x S^2) so that, generically, theresult of Dehn surgery on L is a 3-manifold with two inequivalent genus 2Heegaard splittings, and each of these Heegaard splittings is of Hempeldistance 3.

Berge's distance 3 pairs of genus 2 Heegaard splittings