  We define an equivalence relation between bimodules over maximal abelian
selfadjoint algebras (masa bimodules) which we call spatial Morita equivalence.
We prove that two reflexive masa bimodules are spatially Morita equivalent iff
their (essential) bilattices are isomorphic. We also prove that if S^1, S^2 are
bilattices which correspond to reflexive masa bimodules U_1, U_2 and f:
S^1\rightarrow S^2 is an onto bilattice homomorphism, then:
  (i) If U_1 is synthetic, then U_2 is synthetic.
  (ii) If U_2 contains a nonzero compact (or a finite or a rank 1) operator,
then U_1 also contains a nonzero compact (or a finite or a rank 1) operator.
