Append filter info to URL when using AJAX in 'View' module
What you want to do is manipulate the browser's URL even though there are no page reloads, only AJAX requests taking place.

You are actually in need of the HTML5 History API.

And luckily there seems to be a module available, specific to your case:

https://www.drupal.org/project/views_ajax_history

Give this a try and good luck!