I'm reading through Allen Hatcher's Algebraic Topology, and he mentions that, given a Postnikov tower, the fibration $X_n \rightarrow X_{n-1}$, where $X_n$ and $X_{n-1}$ are CW complexes, can be thought of as an inclusion, and therefore a long exact sequence on homotopy groups can be generated for the CW pair $(X_{n-1},X_n)$.
I was under the impression, that, by definition, two spaces $(X_{n-1},X_{n})$ cannot be a CW pair unless the $X_{n}$ is a subcomplex of $X_{n-1}$, which certainly is not the case here. And I can't imagine how you could generate a long exact sequence in this way. What am I missing here?
I guess, first of all you need to say that any map $f\colon X\to Y$ of CW complexes is homotopic to a map preserving CW structure.
Then again for any $f\colon X\to Y$ (not necessarily for $X_{n}\to X_{n-1}$ in your notations) you can take inclusion of $X$ into the mapping cylinder $cyl(f) = X\cup_f Y $, and this inclusion will be homotopic to $f$, since $X\cup_f Y$ retracts to $Y$. Here $X\cup_f Y = X\times I\sqcup Y/\sim$, where $(x,1)\sim f(x)$. The inclusion $X\to X\cup_f Y$ is given by $x\mapsto (x,0)$.