Virtual Domination of $3$-manifolds

For any closed oriented hyperbolic $3$-manifold $M$, and any closed oriented $3$-manifold $N$, we will show that $M$ admits a finite cover $M^{\mathrm{\prime }}$, such that there exists a degree-$2$ map $f:M^{\mathrm{\prime }}\to N$, i.e. $M$ virtually $2$-dominates $N$.