C and D are equivalent; B and E are equivalent.

Proof of equivalency of C, D using the basic definition of state
equivalency:

For any input seuquence applied to C, D which causes the FSM to
remain in C, D (basically a string of 0's) the outputs are the same
starting from either C or D.

When the input causes the FSM to go to E or B, respectively, the
output remains the same. An input of 0 applied to B or E, causes
the same outputs and a return to C, D respectively.

An input of 1 applied to B or E, causes
the same outputs and a transition to the same state A. Any input
sequence from this point onwards will obviously have the same output
sequence irrespective of whether we were at B or E before reaching A.

Thus from the above reasoning, any input sequence applied to C or
D will either cause the states to circle between C, D, B, E producing
the same outputs OR the FSM will at some ppoint go to state A and
from that point onwards the outputs will be the same.

Thus any input sequence of any length applied to C or D will
result in the same output sequence. Thus C and D are equivalent.

B and E are also equivalent and the proof of their equivalency is 
along similar lines as the above proof of C and D's equivalency.