Reference for Bockstein Homomorphisms / Spectral Sequence for Homology Is there any book for Bockstein Homomorphisms specialising in the case of homology?
So far the books I read (Hatcher, Munkres) discuss it for cohomology. I am aware that it is said to be similar for homology, but as a beginner I don't know how similar it is (Bockstein for homology vs cohomology).
Thanks for any references.
Related question: Is the case of Bockstein Homomorphism for Homology and Cohomology really very similar (e.g. just reverse arrows and replace $H_n$ with $H^n$)? Are there any tricky parts that are different? 
 A: Algebraically there is no major difference between homology and cohomology Bocksteins. Simply replace $C^n$ with $C_n$ (you'll probably want to work through the details explicitly with chains if you are most familiar with singular (co)homology), not forgetting that the homological differential lowers degree (the homological Bocksteins lower the degree). You could check out, say, Rotman's "An Introduction to Homological Algebra" for a decent treatment of the algebraic details (they are treated explicitly in chapter 6, if I recall).
Even topologically the differences are subtle. Recall that (singular) homology is represented by the Eilenberg-Mac Lane spaces $K(A,n)$ ($A$ an abelian group). If 
$0\rightarrow A_1\rightarrow A_2\rightarrow A_3\rightarrow 0$
is a short exact sequence of abelian groups then there is a fibration sequence 
$K(A_1,n+1)\rightarrow K(A_2,n+1)\rightarrow K(A_3,n+1)$
The connecting map $\beta:K(A_3,n)\rightarrow K(A_1,n+1)$ of this fibration (or at least its homotopy class) defines the cohomological Bockstein topologically.
In homology you generally need to work stably, with spectra. In that case the above short exact sequence of abelian groups gives rise to a cofiber sequence of spectra
$KA_1\rightarrow KA_2\rightarrow KA_3$
and this time it is the cofibration connecting map $\beta:KA_3\rightarrow \Sigma KA_1$ that identifies with the homological Bockstein.
