  Detailed analysis of behavior of spin-entangled particle pairs under
arbitrary rotations in their Hilbert space has been performed. It shows a rich
range of varieties (faces) of entanglement in different bases. Analytic
criteria are obtained for the respective faces of an entangled state. The
corresponding conditions generally depend on both the state itself and the
chosen basis. The most important result is revealing a deep analogy between a
spin-entangled electronic qubit pair and momentum-entangled photon pair. Both
cases exhibit coherence transfer from individual particles to nonlocal state of
the system. This analogy allows us to predict certain features of the
interference patterns in spin-entangled qubit pairs.
