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The 301 when changing paths is not builtin EPiServer like it is in Wordpress. You may develop i yourself. Save old paths on PagePublished, PagedMoved events. Then handle all 404s and redirect them to the right page.
Try https://www.coderesort.com/p/epicode/wiki/404Handler The plugin detects all 404 and you can redirect them to the right page.
I will suggest 404 Not Found instead of 410 Gone in your case.
The wheel has already been invented. The Epinova.PermanentLinkKeeper plugin will handle 301s for you when you create, move or delete pages.
http://www.epinova.no/blog/arve-systad/dates/2012/5/epinova-permanentlinkkeeper-released/
Is there a way in Epi to set up addresses to redirect 301 "Move permanently" when we change the path of the page?
Also, when a type of page publish end date is do, i want to display 410 Gone, and not come to login page as default. Ideas?