Spanier-Whitehead duality induces an isomorphism between the cohomological and homological Atiyah-Hirzebruch spectral sequences for finite spectra, extending to Poincaré duality complexes oriented over a ring spectrum.
Kochman, Bordism, Stable Homotopy and Adams Spectral Sequences , American Mathematical Society and Fields Institute, 1996
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A note on Duality and the Atiyah-Hirzebruch spectral sequence
Spanier-Whitehead duality induces an isomorphism between the cohomological and homological Atiyah-Hirzebruch spectral sequences for finite spectra, extending to Poincaré duality complexes oriented over a ring spectrum.