  Any deformation of a Weyl or Clifford algebra A can be realized through a
`deforming map', i.e. a formal change of generators in A. This is true in
particular if A is covariant under a Lie algebra g and its deformation is
induced by some triangular deformation $U_h g$ of the Hopf algebra $Ug$. We
propose a systematic method to construct all the corresponding deforming maps,
together with the corresponding realizations of the action of $U_h g$. The
method is then generalized and explicitly applied to the case that $U_h g$ is
the quantum group $U_h sl(2)$. A preliminary study of the status of deforming
maps at the representation level shows in particular that `deformed' Fock
representations induced by a compact $U_h g$ can be interpreted as standard
`undeformed' Fock representations describing particles with ordinary Bose or
Fermi statistics.
