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Let two Heegaard splittings $V_1 \cup W_1$ and $V_2 \cup W_2$ of a 3-manifold$M$ be given. We consider the union stabilization $M=V \cup W$ which is acommon stabilization of $V_1 \cup W_1$ and $V_2 \cup W_2$ having the propertythat $V=V_1 \cup V_2$. We show that any two Heegaard splittings of a 3-manifoldhave a union stabilization. We also give some examples with numerical bounds onthe minimal genus of union stabilization. On the other hand, we give an exampleof a candidate for which the minimal genus of union stabilization is strictlylarger than the usual stable genus -- the minimal genus of commonstabilization.

On the union stabilization of two Heegaard splittings