Links with surgery yielding the 3-sphere

For any n\ge 2, we give infinitely many unsplittable links of n components in the 3-sphere which admit non-trivial surgery yielding the 3-sphere again and whose components are mutually distinct hyperbolic knots. Berge and Kawauchi gave 2-component hyperbolic links with those two properties. We can also give infinitely many 2-component hyperbolic tunnel number one links with such properties.