  We investigate the asymptotic rates of entanglement transformations for
bipartite mixed states by local operations and classical communication (LOCC).
We analyse the relations between the rates for different transitions and obtain
simple lower and upper bound for these transitions. In a transition from one
mixed state to another and back, the amount of irreversibility can be different
for different target states. Thus in a natural way, we get the concept of
"amount" of irreversibility in asymptotic manipulations of entanglement. We
investigate the behaviour of these transformation rates for different target
states. We show that with respect to asymptotic transition rates under LOCC,
the maximally entangled states do not have a special status. In the process, we
obtain that the entanglement of formation is additive for all maximally
correlated states. This allows us to show irreversibility in asymptotic
entanglement manipulations for maximally correlated states in 2x2. We show that
the possible nonequality of distillable entanglement under LOCC and that under
operations preserving the positivity of partial transposition, is related to
the behaviour of the transitions (under LOCC) to separable target states.
