I would like to proof the following claim:
Let $f: C_{\ast,\ast}\to C'_{\ast,\ast}$ be a map of bicomplexes (differentials anticommute) that is a quasi-isomorphism restricted to each column. Then $f$ induces a quasi-isomorphism on the homology of the associated total complexes.
I know the spectral sequences associated to a bicomplex and I guess they are the key to the proof. Unfortunately I never understood how one can take advantage of those spectral sequences simultaneously.
Thanks a lot for your help!