MLS is going to provide the most accurate, real time data for active listings, closed sales, and expired/cancelled listings. 

Should I withdraw my offer or put a deadline on it so it expires before or shortly after the open houses?

Will it expire by the time repairs are done?

Here's my favorite: Instead of rent increases on your expiring leases, add a monthly utility fee to cover water/sewer/trash/recycling/landscaping as a "community fee."

If you will be moving in after the lease expires, give the new tenant a lease for that period of time.

If so, you'll have to honor those until they expire. 

I'm assuming you'll have you own lease for them to sign upon expiration of their current one so make sure to give adequate notice so it doesn't revert to month to month.So I'd send them a letter introducing yourself as the new property manager/owner/landlord and ask away.

If so you need to wait til the lease expires to raise the rent.

The issue is they both have leases and the earliest expires 05/31/2020.

You can always get tenants out after you close by offering cash for keys, but if the tenants have lease agreements they can refuse to move until the lease term expires!