I am currently working through S.Wangs paper "On the existence of maps of nonzero degree between aspherical 3-manifolds" and got stuck at a part where he claims that for a closed orientable and irreducible aspherical solvmanifold $M$ which is a torus bundle over the circle, any finite covering of $M$ is a torus bundle over the circle as well.
It is unclear to me why that should be the case, as I am not even sure that a finite covering of a fiber bundle always is a fiber bundle. Can you help me understand why this claim should be true?