Page 253, -8 to -4 line Hatcher defines orientation for compact manifolds with boundary.
A compact manifold is $R$_orientable if $M-\partial M$ is $R$-orientable.
If $\partial M \times [0,1)$ is a collar nhood of $\partial M$ in $M$, then $H_i(M,\partial M;R)$ is naturally isomorphic to $H_i(M-\partial M, \partial M \times (0,\varepsilon);R)$
I do not see how we have this isomoprhism.
Lemma 3.27 (page 236) gives a relative fundamental class $[M]$ in $H_n(M, \partial M;R)$ restricting to a given orientation at each point of $M - \partial M$.
What is a "relative fundamental class" and how does this conclusion follow? I am lost with the two described steps.