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Peter Scott, in his survey "The Geometries of 3-Manifolds", states that the family of spheres defining the decomposition of a given 3-manifold $M$ into primes is not unique up to isotopy even when $M$ is orientable. Can someone give an example for this?

Mustafa
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    I think such a family of spheres is unique up to slide homeomorphisms. Maybe you can find some more insights by googling this. Understanding the slide homeomorphisms will basically teach you everything about what could potentially go wrong in the uniqueness you described. – Daniel Valenzuela Jul 21 '16 at 17:31
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    you can profit a lot by reading Orlik's Seifert Fiber Spaces – janmarqz Jul 21 '16 at 23:58

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