  Motzkin paths with air pockets (MAP) of the first kind are defined as a
generalization of Dyck paths with air pockets. They are lattice paths in
$\mathbb{N}^2$ starting at the origin made of steps $U=(1,1)$, $D_k=(1,-k)$,
$k\geq 1$ and $H=(1,0)$, where two down-steps cannot be consecutive. We
enumerate MAP and their prefixes avoiding peaks (resp. valleys, resp. double
rise) according to the length, the type of the last step, and the height of its
end-point. We express our results using Riordan arrays. Finally, we provide
constructive bijections between these paths and restricted Dyck and Motzkin
paths.
