Whether you started a new year lease over or merely changed the address of your old lease is not clear. On the one hand, L told you "everything would be exactly the same except the address." This implies that the original dates & pet deposit transfer over. On the other hand, the new lease specifies that it runs for a year. You made a mistake when you signed the back page of the lease without even seeing the first pages. You'd have caught these problems & wouldn't be writing us now. If both of you honestly believe your interpretation is correct, then you never had a meeting of the minds & never entered into a contract at all. Thus, you'd have no written lease & would be a month-to-month tenant who could leave on a month's notice.
I tend to think that the old lease dates apply. L had a duty under the old lease to protect your right of quiet enjoyment of your apt. When you complained of noisy neighbors, L had 2 choices: solve the problem or be in breach of the lease. L's solution was to move YOU instead of the neighbors. As this move was intended to prevent L from breaching the old lease, it is likely that L was giving you the new apt for the remainder of your term at the old place. Otherwise, L will owe you damages for breaching the old lease (& you can sue L to collect). L probably just made a msitake when he filled in the termination date & will be all too willing to correct it (in writing) when you point out all the ways L has screwed himself.
Also, since the new apt is a substitute, the deposits should transfer over to the new place. If the new lease is not a continuation of the old lease, then L had to send you a statement of deductions from the deposit within 30 days or L owes you a double refund. [Ohio Code, § 3733.18 Security deposit] If you point this out to L (AFTER the 30 days has passed), L has to back down or he's shot himself in the foot! By waiting until the full 30 days has passed, you give L every opportunity to behave in a fashion consistent with a mutual agreement to terminate the old lease & enter into a new lease.
You can also argue that the lease was unconscionable, since L insisted you sign the back page without allowing you to see the rest of the lease. If L's actions were unconscionable, the lease is void.
Talk to L & ask him if he wants to acknowledge that the old lease dates carry over, or if he wants you to sue his ass.
Regarding the pet deposit check: you have a cancelled check as a receipt. Send L a copy & tell him you're not paying the deposit twice. (Again, if L is going to require a new deposit, he has to return your old deposit within 30 days or pay double.) It would be even better if you have a receipt from L that calls the money the pet deposit, or if the old lease notes that the deposit was paid.
Good luck.
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This is not legal advice and you are not my client. Double check everything with your own attorney and your state's laws.