Are there transitive ciphers (either symmetric and asymmetric) Say Alice has information that's already encrypted with Bob's key.
She wants Bob to decrypt it without knowing what he just decrypted.
So she encrypts it with her key and sends it to him, he decrypts with his key, and sends it back and she decrypts it with her key.

Is there a block cipher where this would work?
Actually, there's the Pohlig-Hellman cipher (dating back to the 70's) that can do precisely this; it works like this:


There's a large public prime $p$ (for which the DLOG problem is hard)
The secret key is an integer $x$ that is relatively prime to $p-1$
To encrypt a message $M$ with key $x$, we compute $C = M^x \bmod p$
To decrypt a message $C$ with key $x$, we compute $M = C^{x^{-1} \bmod p-1} \bmod p$


It should be clear that the encryption and decryption processes (for a fixed key) are inverses of each other, and that this allows Alice and Bob to do precisely what you asked for; if Alice has $M^b$, she can give Bob , $(M^b)^a = M^{ab}$; Bob computes $(M^{ab})^{b^{-1}} = M^a$, and send that back to Alice, who can then recover $M$