A question about the index of vector field

Question

$M$ is the boundary of a compact manifold $U$: $M = \partial{U}$, $\mathbf{v}$ is a unit vector field on $M$, how to prove that if $\mathbf{v}$ can be extended to be a nonvanishing vector field on all of the interior region $U$, then $\operatorname{index}(\mathbf{v})=0$?

Answer 1

Since $\mathbf{v}$ can be extended to a nonvanishing vector field on $U$, $\mathbf{v}$ on $M$ can be shrunk continuously into small sphere around any point in U, where vector field v behaves like a constant vector field and has index 0, so the original vector field on M should have index 0.