How do I withdraw my petition to cancel or my notice of opposition?

You must file a document stating what you wish to do. However, once an answer is filed, if you want the matter dismissed without prejudice, you will need to obtain the written consent of the other side; and, of course, you need to serve the other party to the proceeding with a copy of anything you file. If you do not obtain written consent, the proceeding will be dismissed with prejudice.