Let $M$ be a hyperbolic 3-manifold with no rank two cusps admitting an embedding in $mathbb S^3$. Then, if $M$ admits an exhaustion by $pi_1$-injective sub-manifolds there exists cantor sets $C_nsubset mathbb S^3$ such that $N_n=mathbb S^3setminus C_n$ is hyperbolic and $N_nrightarrow M$ geometrically.