  We here present two different hierarchies of PDEs in 1+1 dimensions whose
first and second member are the shallow water wave Camassa-Holm and Qiao
equations, correspondingly. These two hierarchies can be transformed by
reciprocal methods into the Calogero-Bogoyanlevski-Schiff equation (CBS) and
its modified version (mCBS), respectively. Considering that there exists a
Miura transformation between the CBS and mCBS, we shall obtain a relation
between the initial hierarchies by means of a composition of a Miura and
reciprocal transforms.
