Give an example of complexity classes $M$ and $N$ and oracles $A$ and $B$ such that  1. $M^A=N^A$ and  2. $M^B\neq N^B$ and 3. $M \neq N$.
Complexity class separation in the presence of relativization barriers
cc.complexity theory;reference request;complexity classes;oracles
I found an answer in Theorem 3 in Hartmanis, Chang, Chari, Ranjan, Rohatgi. They show that relative to EXPSPACE-complete languages, PCP(log) = PCP(poly). Since PCP(log) = NP  NEXP = PCP(poly), we are done.