  Zero curvature formulations, pseudo-potentials, modified versions, ``Miura
transformations'', and nonlocal symmetries of the Korteweg--de Vries, Camassa--
Holm and Hunter--Saxton equations are investigated from an unified point of
view: these three equations belong to a two--parameters family of equations
``describing pseudo-spherical surfaces'', and therefore their basic
integrability properties can be studied by geometrical means.
