The verb translated as "persecute" means both "chase away" and "seek after." The best way to translated this word is "hound" because it covers both meanings. The use of "this city here" makes the Greek seem like Jesus is referring to a specific city, perhaps brought up in a question that was not recorded.
The verb translated as "going over/finish going/reached" actually means "completed" and it is the verb form of the word translated as "end" in the previous verse.
Christ's Words in Matthew as a Guide to 40 Days of Prayer.