What is the best reference for spectral sequences for mathematicians who are not experts at the subject, but would just like to open a book and find the SS they need, without going in to deep.

I'm looking for a concise encyclopedic approach, in which theorems are stated with the minimum possible hypotheses and clearly written assumptions, but with sufficient explanations/definitions/facts about the surrounding theory of a SS, so that I won't make a mistake using it by misunderstanding the statement. A book that is intended for interested 'visitors', not 'natives' of the theory.

For example, Weibel's *Homological Algebra* and Davis&Kirk's *Lecture Notes in Algebraic Topology* and *The Stacks Project* are extremely useful and well-written, though I find McCleary's *A User's Guide to Spectral Sequences* and Rotman's *An Introduction to Homological Algebra* less user-friendly. On the wiki page, there are mentioned several interesting examples of SS.

Where can I learn about the Kunneth SS? I assume the formulation should be similar to: If and $A_\ast,B_\ast$ are chain complexes of $R$-modules, then there are spectral sequences of modules $E^2_{p,q}=\bigoplus_{q'+q''=q}Tor_p^R(H_{q'}A_\ast,H_{q''}B_\ast)\Rightarrow H_{p+q}(A_\ast\otimes B_\ast)$ and $E_2^{p,q}=\prod_{q'+q''=q}Ext^p_R(H_{q'}A_\ast,H_{q''}B_\ast)\Rightarrow H_{p+q}(Hom(A_\ast, B_\ast))$. But what are the minimal assumptions for this to hold? I'd like to have a formulation, such that when $R$ is hereditary, we get the Kunneth shhort exact sequences. I can't find this in any of the mentioned books. Also, if $A_\ast$ and $B_\ast$ are the singular chain complexes, is there a similar SS of algebras for cohomology?

Where can I learn about the Mayer-Vietoris SS of an open covering, Cartan–Leray SS of a quotient space, van Kampen SS of a wedge space, etc.? I feel there's a huge potential with SS, but they are somewhat inaccessible to people from other areas of mathematics. I'd just like to have systematic statements in the form $E_{p,q}^2\ldots\Rightarrow\ldots$ and $E^{p,q}_2\ldots\Rightarrow\ldots$ and explanations of what each of the objects in the formula is, so I can get my hands real dirty with fun computations, appropriate for a novice. Davis&Kirk is perfect for that, I wish the book were ten times longer, so I could devour it all.

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