Given a tower of fibrations of homotopy types, its degreewise homotopy groups naturally form an exact couple. The induced spectral sequence is the spectral sequence of the tower.
Paul Goerss, Rick Jardine, section VI.2 (in the 1999 version) or section VII.6 (in the 1996 version) of Simplicial homotopy theory
Mike Shulman, spectral sequences (2013)
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