Fisk isn't going after Spider-Man and it's easy to see why
Ever since the creation of the AVTF, I've seen people wondering why Fisk isn't going after Spider-Man, despite hunting down every other vigilante in the city. It's especially weird, considering Spidey is THE NYC vigilante. You'd think he'd be their prime target.
Yes, he did name him on live TV, but he isn't taking direct action against him. In fact, it seems like the Task Force isn't even remotely interested in capturing the Webslinger. He somehow seems exempt from Fisk's crusade. The Mayor seems to be all bark and no bite when going against him. But why?
Well, to me the answer seems incredibly obvious. He's not a vigilante, he's a legitimate superhero. Let me explain.
Out of all the vigilantes, Spidey is the only one who has legitimately worked with the Avengers, which is as close as you can get to being an "official hero". Avengers records also show that he was the only NYC vigilante present at the Battle of Earth. He had a hand in saving the whole universe from Thanos.
Secondly, Spidey just had a very public trial where he was accused of murdering a fellow "hero" (still can't believe that fraud has supporters), which ended in all charges being proven false.
Touching Spider-Man right now is like chucking your ratings off a cliff. He'd have to somehow convince the public that the guy who helped save the whole universe is "dangerous". Do you see that happening? Because I sure as hell don't.
Not to mention, if Spidey gets charged and they turn out to be false yet again, then his reputation would be stronger than ever. Meanwhile, for our dear Mayor, it'd be legitimately over. It wouldn't surprise me if going after him resulted in Captain America making a visit to the Mayor's office. I'm sure he doesn't want that.
TL;DR: Mayor Fisk probably considers Spider-Man to be too hot to handle and knows that trying to bring him in would be career suicide. That's why he isn't sending the AVTF to capture him.