There are inconsistencies between all the games actually. We all praise Devil May Cry 3 for its great story (myself amongst them) but it isn't as connected as it could have been with the original Devil May Cry.
The first Devil May Cry, starts with Trish entering Dante's shop. One of the lines says: "You are the man who lost a mother and a brother to evil, 20 years ago? The son of the legendary dark knight? Mr Dante?"
What does this suggest? That in the original plot, in the same attack that killed Eva, Vergil was probably abducted and brainwashed/turned into Nelo Angelo. In the first game, somehow I got the idea that the scenario-writers wanted Dante to only know of Vergil as a kid (if you remember, the moment he realizes he just defeated his brother, the only memories that come to his mind are those from when they were children). Even when Vergil took of the Nelo Angelo helmet, Dante didn't get a clue. If he had seen Vergil as a grown up, he should have been able to recognize it. His face without the helmet isn't as distorted as the corrupted-Vergil costume, so for me that just shows that Dante never saw Vergil's adult face up until then.
Even when he meets Vergil in the Devil May Cry novel, which was considered canon, before Devil May Cry 3 appeared, Vergil's face is wrapped in bandages and he already works for Mundus, so it fitted better than Devil May Cry 3 does. We also learnt about Ebony & Ivory, Tony Redgrave and .45 Art Warks. Though considering the guns, it still has somewhat of a plothole as even Sparda's guns Luce & Ombra share the same carvings.
Then Devil May Cry 3 appears and again at the beginning, the moment Dante learns that Vergil is seeking him he even mentions that they had not seen each other for only a year. And after that goes and creates a great story about how Dante got the Force Edge and how he came up with the Devil May Cry name for his shop.
The Devil May Cry 3 Manga tried to explain about how Vergil met Arkham, how Arkham became a demon, when was that *one year ago* meeting between Dante and Vergil and how Lady started her Devil Hunting bussiness. As the creator never managed to finish the story though, it is kinda silly. Nice, but lacking.
Devil May Cry 2, kinda passes, because it could be just a story very far away from the other games. Though back when it first appeared, we were all wondering why the shop's name had changed from Devils Never Cry, to Devil May Cry again. No clue was given.
Devil May Cry 2 novel, was somewhat of a side-quest. An extra mission of Dante. I don't even see why Capcom made it non-canon. It doesn't negate any of the knowledge we already have. But oh well.
Devil May Cry 4 doesn't really do anything to affect the Devil May Cry story. It just exists, throws Nero to us, making things even more complicated, but other than that it's ok. Trish is in the shop with Dante, they have the sword Sparda in the wall, so yeah, it kinda shows that it's after the first Devil May Cry, and since Lady appears too, it connects with Devil May Cry 3 as well. It's kinda like the Devil May Cry 2 novel. A side-story, one of Dante's missions. And then came they Devil May Cry 4 novel, hinting (almost saying it directly) that Nero could be Vergil's son.
Same with the Devil May Cry Anime. Regular Dante missions. I don't know whether Patty or Morisson are considered canon, but no matter. They don't affect the story in great part so they might as well be.
My point is this: In the Devil May Cry Universe (not DmC of course) because each game, book, manga, story, is written by a different person, they WILL be inconsistencies. It's impossible not to be. Each guy interprets the story differently, and obviously most of them are not even dedicated enough to research the story as a whole before adding their new stuff, complicating things even more.
So something like "what is canon" and "what it is not" is kinda hard to judge. We should either have our personal thoughts of what canon is, or just follow Capcom's lead, who seems to change its mind all the time. And now it's in a state where it might abandon the whole "old" Devil May Cry universe, for their new DmC project. I'm not saying they will. I'm saying they might.
My opinion? Everything is canon. Dante did all these things, was Tony Redgrave, met Vergil 3 times, visited other worlds etc etc. Because that's the way I like it, no matter what Capcom says.
What's yours?