By default, your Markbook begins on the main tab. Any filters applied on this tab will remain when the Markbook is navigated away from. However, additional tabs can be created to host different filters.
To create a new Markbook Tab, click the + next to Main at the bottom left of the Markbook.
The tab can be renamed by clicking its name and typing a new one in. Any filters created in each tab will remain unless later changed.