My advisor once told me that the following statement (which I read in Ravenel's Complex Cobordism and Stable Homotopy Groups of Spheres) was a Folk Theorem:
For $p>2$ and in a certain range, the Adams Spectral Sequence coincides with the homology Bockstein spectral sequence
It turns out the range is $t<(2p-1)s-2$, and a reference is Haynes Miller's paper
