Let d be a square-free positive integer, let Od denote the ring of integers in Q( √ −d), and let Qd denote the Bianchi orbifold H/PSL(2,Od). A non-compact finite volume hyperbolic 3-manifold X is called arithmetic if X and Qd are commensurable, that is to say they share a common finite sheeted cover (see [26] Chapter 8 for more on this). If N is a closed orientable 3-manifold and L ⊂ N a link, ...