Who shall be entitled to cenvat credit?

If it's a Finance lease, then definitely Mr B would be paying the maint chgs & he would get the Cenvat Credit.

And What if it is an operating lease??

Don't think so the lessee would be entitled, as all the risks & rewards are with the lessor unlike an finance lease.

it is an operating lease and the lease deed contains this provision - " However,any tax in force at present including but not limited to service tax or that may be levied in future by any local, state or central government/authority which is applicable to the Lessee or in a nature applicable to the Lessee shall be paid by the Lessee."

The property is owned by the lessor, Mr. A. He would be eligible for credit. Not the lessee. 

In the deed, it is mentioned that the payment has to be made by the lessee but the credit of the same will be available with Mr A only.

can the credit be passsed on by Mr.A to Mr.B?

I dont think so. You cannot pass on cenvat credit without being an Input Service Distributor.

kk...thanxx