Virtual Domination of 3-manifolds III

We prove that for any oriented cusped hyperbolic 3-manifold $M$ and any compact oriented 3-manifold $N$ with tori boundary, there exists a finite cover $M^{\mathrm{\prime }}$ of $M$ that admits a degree-8 map $f:M^{\mathrm{\prime }}\to N$, i.e. $M$ virtually 8-dominates $N$.