  We consider a two parameter family of Drinfeld twists generated from a simple
Jordanian twist further twisted by 1-cochains. Twists from this family
interpolate between two simple Jordanian twists. Relations between them are
constructed and discussed. It is proved that there exists a one parameter
family of twists identical to a simple Jordanian twist. The twisted coalgebra,
star product and coordinate realizations of the $\kappa$-Minkowski
noncommutative space time are presented. Real forms of Jordanian deformations
are also discussed. The method of similarity transformations is applied to the
Poincar\'e-Weyl Hopf algebra and two types of one parameter families of
dispersion relations are constructed. Mathematically equivalent deformations,
that are related to nonlinear changes of symmetry generators and linked with
similarity maps, may lead to differences in the description of physical
phenomena.
