In what follows $M$ will be a manifold (without boundary, for simplicity) and $C\subseteq M$ will denote a compact subset. In the paper Deformations of spaces of imbeddings Edwards and Kirby prove the following:

Corollary 1.2: Let $h_t:C\to M$ be an isotopy such that it has an extension to a neighbourhood $U$ of $C$. Then there exists an isotopy $H_t:M\to M$ such that $H_0=1_M$ and $h_t=H_t\circ h_0$.

I would be interested in applying this Corollary to the following situation: $M$ is a compact complex manifold and $C=C_1\cup\dots \cup C_n$ is a normal crossing divisor.

Question: Does any one know if I can apply the Corollary to the situation I am interested in?

My attempt: In this paper https://arxiv.org/pdf/1706.09539.pdf the authors prove that the inclusion $C\to M$ is a cofibration (Theorem 1.1) (they work in an equivariant setting, so just pretend the the group in question is the trivial group). This is not exactly what I was searching for, because it ensures only that I can extend the isotopy to an homotopy.