Several spectral sequences coming from geometry have a "degree of freedom" in choosing the coefficients (say an abelian group $A$). This applies fo example to the Serre spectral sequence and to the spectral sequence of cosimplicial spaces.
Is there a way of comparing the spectral sequences of different coefficients? This should be a generalization of the universal coefficient theorem (that applies to the early pages, but then gets somehow "lost" when turning pages).
If you also have a reference for this, it would be great.