Let $M$ be a closed smooth submanifold of $N$. It is well known that tubular neigbourhoods of $M$ are diffeomorphic to the normal bundle of $M$ in $N$ and therefore to each other. Are they smoothly isotopic? I think I know how to prove that they are, but having a reference would be nice.

If they are not, how is it enough to just assign a framing to a knot to obtain a surgery? Is the pair (framing, sphere embedding) enough for high dimensional handle attachments/surgery?

Definition: for a Riemannian metric $g$ on $N$, let $\nu_{g,\epsilon}(M)$ be the $\epsilon$-neighbourhood of $M$ in $N$. For $\epsilon$ small enough, $\nu_{g,\epsilon}(M)$ is a tubular neighbourhood.

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