If my insurance is from Tanghai, can I transfer it to Tangshan?

You can totally handle it. You are from Tanghai, and you are under the jurisdiction of Tangshan City. It will be easier to handle. You can go to Tangshan Social Security Bureau from your work unit in Tangshan to handle your transfer procedures. If you don't have a work unit, you can go to Tangshan Social Security Bureau to handle the reception procedures yourself, and then go to Tanghai to handle the transfer relationship.