  We construct the dagger realization functor for analytic motives over
non-archimedean fields of mixed characteristic, as well as the
Monsky-Washnitzer realization functor for algebraic motives over a discrete
field of positive characteristic. In particular, the motivic language on the
classic \'etale site provides a new direct definition of the overconvergent de
Rham cohomology and rigid cohomology and shows that their finite dimensionality
follows formally from the one of Betti cohomology for smooth projective complex
varieties.
