  We consider new Abelian twists of Poincare algebra describing non-symmetric
generalization of the ones given in [1], which lead to the class of
Lie-deformed quantum Minkowski spaces. We apply corresponding twist
quantization in two ways: as generating quantum Poincare-Hopf algebra providing
quantum Poincare symmetries, and by considering the quantization which provides
Hopf algebroid describing the class of quantum relativistic phase spaces with
built-in quantum Poincare covariance. If we assume that Lorentz generators are
orbital i.e.do not describe spin degrees of freedom, one can embed the
considered generalized phase spaces into the ones describing the
quantum-deformed Heisenberg algebras.
