  In the present paper, we define a notion of good coverings of Alexandrov
spaces with curvature bounded below, and prove that every Alexandrov space
admits such a good covering and that it has the same homotopy type as the nerve
of the good covering. We also prove the stability of the isomorphism classes of
the nerves of good coverings in the non-collapsing case. In the proof, we need
a version of Perelman's fibration theorem, which is also proved in this paper.
