The simplicial volume conjecture for open 3-manifolds

Let $SV(3)$ be the set of simplicial volumes of closed $3$-manifolds, and let $SV^{\text{lf}}(3)$ be the set of simplicial volumes of all $3$-manifolds without boundary. Here simplicial volume is understood in the locally finite sense for open manifolds, and $\infty$ denotes infinite simplicial volume.

Simplicial volume conjecture for open 3-manifolds.

$$SV^{\text{lf}}(3)=SV(3)\cup\{\infty\}.$$

The equality would completely determine the set of simplicial volumes of open $3$-manifolds. The corresponding result is known for tame open $3$-manifolds, but the general case remains open.