Teach me the match-up, Frantic!
Haha, it's kind of hard to put it into words, but I'll give it a shot.
First off, zone with your normals. Use as many of them as you can - s.L, s.M, cr.M, s.H, Stinger, j.M and j.H are all great normals to out range Nova, and using them in the right spots will really force Nova to reconsider how he approaches. I find j.M to be especially good - the speed and range it has means Dante can bop characters from a larger range than most, and he has less to fear of the box dash j.H OS. Additionally, well placed normals can hit Nova's slide, especially something like Dante's own cr.M, you just have to be careful that you use them in the right spots.
After that, Air Play is your friend, especially if Nova is using a non-Bolts assist. It shuts off his air approach, and can hinder his grounded approach. There's a sweet spot for every position Nova can be in(full-screen, mid-screen and nearby shouldn't be used unless you know you're going to be able to get it out before they can punish you), and it takes some practice to get it. Generally, from full screen, you want to be at semi-double jump height(semi as in, when you double jump, you don't let yourself reach its peak) when you use it. If you position it right, it'll hit any air approach from Nova, it'll hit assists when they're called, and you can even time it so it'll go in between Bolts to hit Strange so the second bolt doesn't come out. Additionally, you should try to air-to-air Nova with j.M followed by a delayed Air Play. The delay will allow Air Play to catch forward, neutral and back techs. It'll either hit them(because they're mashing or just holding forward) or they are forced to block which will result in either pressure(with a box dash j.H) or distance to zone. Watch out for Gravimetric Pulse M(with Red Health), as the really smart Nova's will try to snipe Air Play with it(which is like, 1 out of 1000 Novas, but the option is there and should be at the back of your mind so you don't get surprised).
Hammer is also super useful in the matchup(since Nova either wants to box dash j.H/throw you, go under you and mash s.L, or try to slide as you're coming down), but it's hard for me to talk about where to use it. 9/10 times, I use it on instinct. "Oh, he's about to do this here, so Hammer will beat it." It's just a gut feeling that I go on, and it usually works out. After playing a lot of Nova(and I have TONS of Nova experience), you start to pick up on tactics in certain spot that you'll just know when to use it.
Drive/Crystal should only be used when you start noticing Nova approaching from the ground rather than the air. Drive is good for Nova/Bolts, Crystal is generally better in every other Nova matchup. You don't want to use either of them too much at the mid-range, as that's prime position to get hit with a slide, but liberal usage will do good. You should basically use them when you've got them scared of box dashing, but have them scared of getting hit with Dante's sword normals.
Teleport > back box dash j.H when you see them box dash and you're nearing the corner. It's a more or less free escape that'll give you plenty of space to work with. This is an underutilized tactic in general for Dante, and when I use Air Trick, it's generally for this purpose. Just gotta watch out for people who start noticing this fact and try to bait it... but then you can start baiting the bait, and yeah.
When you have them block something relatively close, pressure him as much as you can, but don't be afraid to back off if you're starting to get pushed out and any more offense would be risky. Additionally, when they're getting close to you, don't be afraid to switch from zoning to immediate rushdown. It catches tons of people off guard where they're expecting a defensive action and get an offensive action.
Use s.L to anti-air Nova. It doesn't lead to combo, but it'll reset the situation in Dante's favor. People are often too concerned with anti-airing into a combo and don't utilize the fact s.L resets things in Dante's favor. It's frankly the best normal Dante has for catching Nova, and it's dumb not to use it. Try to s.L > Bold Move into offense or retreat, s.L > Crystal to make sure he doesn't try to immediately recover and hit you, etc, etc.
As far as assists go, can't really comment. I tend to use Low Voltage a lot in the matchup, since it'll catch Nova doing anything on the ground or normal jump height, and it'll hit pretty much every assist he could call if it comes out before getting hit. Vajra tends to sit on the back burner for that matchup. Although, if I was running Doom, I'd probably pick Hidden Missiles against Nova. Enhances Dante's zoning game, and allows him to play a bit more recklessly.
Stinger means Nova can't try to keepaway with Javelins + Gravimetric Pulse H. Reverb Shock can be good in the mid-range to catch Nova about to do something. cr.M can be used to preemptively catch Nova's cr.M or grouned approach. Raw launch ain't a bad anti-air against Nova. Jet Stream can be used to go under box dash j.H if you see it coming. Jam Session can be good, too. Especially if you notice the Nova starts trying to approach from the super jump height(which a lot of the crappy ones will try to do).
There's tons of other things you can do, but they're situational and generally only come into play when the matchup becomes a player vs player matchup rather than a character vs character matchup. Dumb shit like Cold Shower >>> Prop Shredder 'OS' where if they slide they get bopped into combo, and if they try to box dash you go right into Prop Shredder and it will lead into a combo(and be sure to call something like Vajra right after Prop Shredder activates to make it safe!). That sort of thing only comes into play when you really start breaking down the opponent's playstyle, and start getting into their head.