I have two Gmail accounts, one is personal, the other is business. I have enabled forwarding on the business one, so I get those mails to my personal email account. Sometimes I delete some e-mails from my personal account which have been forwarded from the business account, but they are not deleted from the business account. I want the actions I take in my personal mail to be synced to my business account. Is there a way to do this?
You can't sync between accounts. Sync works between an e-mail client on your computer or mobile device and the account on the server (using IMAP). But forwarding or POP fetching can not sync between server accounts.
This Chrome extension may work for you: Gmail Label and Email Sharing