In my work, I often need to toggle between two tabs, often collecting data from one tab and using it in another. A quick way to move between adjacent tabs without using the mouse is with Command-Shift-]. Multiple hits of Command-Shift-] will move you right along the Tab Bar. To move left, use Command-Shift-[. Combining both of these, you can use Command-Shift-] and Command-Shift [ to quickly toggle between adjacent tabs.
An often handy trick is to move a tab to its own window or to another open window. To do this, simply drag the tab down and over. If you want the tab in a new window by itself, just drag the tab down into the main page. If you want to move it to an open window, drag it to that window. (You may need a larger screen to do this so your Safari windows aren't overlapped.)
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