That said, what you should do is bookmark a link using the MO search function. For example, if I just want to see questions tagged [ap.analysis-of-pdes] and [fa.functional-analysis], I can enter the url
http://mathoverflow.net/questions/tagged/ap.analysis-of-pdes or fa.functional-analysis
(note that the two tags are separated by the word or surrounded by spaces; you can equivalently use the HTML escaped %20or%20 instead.) The above url brings up this link which shows for me the thirty active questions having at least one of those two tags.
And if you want to instead search of [ap] and not [mp.mathematical-physics], use the minus sign operator like this:
http://mathoverflow.net/questions/tagged/ap.analysis-of-pdes -mp.mathematical-physics
(put a space between the tags, and the minus sign - in front of the undesired tags). So you will just have to craft (once and for all, I hope) your own custom search string.
Note unfortunately that a search string cannot consist of just ignored tags. You will have to specify also tags you want to see. See this discussion on Meta.SO.
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