The Wikipedia page for Borel-Moore homology states that for a locally compact set $X$ and a closed subset $Z$, if we write $U = X \setminus Z$ we have the following long exact sequence
$$\cdots \to H^{BM}_n(Z) \to H^{BM}_n(X) \to H^{BM}_n(U) \to H^{BM}_{n-1}(Z) \to \cdots$$
The reference given there is Iversen's book, where the definition of Borel-More is the sheaf theoretic one. However, I'm interested in the definition via locally finite chains, and was wondering if there is a description of the boundary map in these terms. I have some idea of what it might be, thinking of $\overline X$ as a compactification of $U$ with whose boundary is $\partial X \cup Z$, but I'm not being able to fill in the details and furthermore the compactification is a bit inconvenient for the purpose I have in mind, so it would be nice to find a description directly in terms of locally finite chains.
