A four dimensional mapping Torus Parallelizable?

Question

I want to show that under certain conditions a four dimensional mapping torus is parallelizable. Let $X$ be a 3 dimensional, compact, orientable Riemann manifold. We know that every such manifold is parallelizable. That means we have three vector fields $X_{1}, X_{2}, X_{3}$ such that they form a basis at any point. Let $f: X \to X $ be a diffeomorphism such that ($f_{p})_{*}X_{i}(p)=X_{i}(f(p))$. Now can I conclude that the mapping torus $M_f$ is parallelizable?