  We re-examine all the contractions related with the ${\cal U}_q(su(2))$
deformed algebra and study the consequences that the contraction process has
for their structure. We also show using ${\cal U}_q(su(2))\times{\cal U}(u(1))$
as an example that, as in the undeformed case, the contraction may generate
Hopf algebra cohomology. We shall show that most of the different Hopf algebra
deformations obtained have a bicrossproduct or a cocycle bicrossproduct
structure, for which we shall also give their dual `group' versions. The
bicovariant differential calculi on the deformed spaces associated with the
contracted algebras and the requirements for their existence are examined as
well.
