  A general construction is given for a class of invertible maps between the
classical $U(sl(2))$ and the Jordanian $U_{h}(sl(2))$ algebras. Different maps
are directly useful in different contexts. Similarity trasformations connecting
them, in so far as they can be explicitly constructed, enable us to translate
results obtained in terms of one to the other cases. Here the role of the maps
is studied in the context of construction of twist operators between the
cocommutative and noncocommutative coproducts of the $U(sl(2))$ and
$U_{h}(sl(2))$ algebras respectively. It is shown that a particular map called
the `minimal twist map' implements the simplest twist given directly by the
factorized form of the ${\cal R}_{h}$-matrix of Ballesteros-Herranz. For other
maps the twist has an additional factor obtainable in terms of the similarity
transformation relating the map in question to the minimal one. The series in
powers of $h$ for the operator performing this transformation may be obtained
up to some desired order, relatively easily. An explicit example is given for
one particularly interesting case. Similarly the classical and the Jordanian
antipode maps may be interrelated by a similarity transformation. For the
`minimal twist map' the transforming operator is determined in a closed form.
