Virtual infinite Betti number conjecture for 3-manifolds

Let $M$ be an orientable, irreducible closed $3$-manifold with infinite fundamental group. Virtual infinite Betti number conjecture. Either $\pi_1(M)$ is virtually solvable or $M$ has finite covers with arbitrarily large first Betti number. The claim strengthens virtual positive Betti number in the nonsolvable case; the source provides no resolution status.