MQV protocol and man-in-middle attack Why MQV is said to be an “authenticated Diffie-Hellman” protocol? The process in the picture shows nothing about authentication. Besides, a man-in-middle can impersonate B to negotiate with A, because A does not verify the identity of B.
The process in the picture shows nothing about authentication

You are correct in that explicit signatures are never sent, however the exchange involves so-called implicit signatures. You will note that the derivation of the shared secret relies not only on the ephemeral session keys $(x,X)$ and $(y,Y)$, but also the long-term authentication keys $(a,A)$ and $(b,B)$. The concept then is to create a system where knowledge of both $x$ and $a$ is required for Alice to construct the correct shared secret. If either party does not know both the private keys, then they will disagree on the established secret, and thus the exchange will fail.
The importance of this in AKE is that we construct a scheme which retains many of the desirable traits of ephemeral key exchange whilst still having a long-term key which can be used as the basis for a certificate. If the protocol succeeds (assuming there are no good attacks on MQV), the parties can be assured that they know the correstponding private keys to their long-term public keys $A,B$.

Besides, a man-in-middle can impersonate B to negotiate with A, because A does not verify the identity of B.

You're correct; the scheme in its raw form, without a trusted third party, is vulnerable to someone simply publishing their own long-term keys whilst purporting to be a legitimate party. However, this is not the purpose of authenticated key exchange in the form presented here. The purpose of authenticated key exchange as presented here is to verify private key ownership, which is different to identity. Much like how a digital signature does not actually prove that Alice signed something, only that someone who knows the private key corresponding to the public key you believe to be Alice's signed it.
We can construct a system which verifies identity from a system that verifies private key ownership with the aid of certificates and a T3P in the form of a CA.
This is not to say there are not attacks on MQV which can undermine some aspects of its intended goals
B. Kaliski showed that MQV is vulnerable to a Unknown Key Share attack whereby Eve can trick two participants into performing a key exchange where:

Alice knows she is performing a key exchange with Bob
Bob thinks he is performing a key exchange with Eve

Note that Eve does not actually discover the shared secret, and this can be mitigated with a key confirmation step, where participants prove to each other that they know the shared secret, but the MQV protocol does not force this. HMQV is a version of the protocol which aims to stop the attack whilst not requiring explicit key confirmation.