Let $M$ be a closed connected orientable 3-manifold. Then Kneser tells us that there is a decomposition $M = P_1 \sharp \cdots \sharp P_k$ of $M$ into prime manifolds. Milnor tells us that if $M = Q_1 \sharp \cdots \sharp Q_l$ then $k = l$ and the $Q_i$ are homeomorphic to the $P_j$ in some order.
Is there any theorem that tells us to what extent the spheres that give a prime decomposition are unique? They are not unique up to isotopy at all bit I was wondering if there was some set of moves for getting between any set of prime decomposing spheres.