Currently in the series, not much is known after the death of Eva and before Vergil's revival of the Temen-ni-Gru.

In Devil May Cry, Trish stated that Dante was a "man who lost a mother and a brother to evil twenty years ago". Eva was killed by what most possibly are demons who were seeking revenge over Sparda's closure of the gate between the demon and human worlds. However, Vergil was "lost" in a different way. In general, Vergil admires his father for unknown reasons. Seeing that he could not save or protect his mother, he probably began lusting for power and was succumbed by evil while doing so.

Whatever happened after Eva's death is also unknown. Vergil had also apparently left Dante for quite a few years after, again, for unknown reasons. Eventually, Dante sets up a demon hunting business, and the Temen-ni-Gru is revived shortly after.

  ± "Remember what we used to say? Jackpot!"
So, what happened during the time in-between? Who knows, but here are my speculations. After Trish's death, the brothers probably continued to live together. During which Vergil gradually became insane over the idea of power. A line which was cut out of the Devil May Cry 3 game in the scene prior to the brothers pulling the triggers to Ebony & Ivory to end their fight with Arkham was "Remember what we used to say when we beat the shit out of that guy?"....

Considering that Dante having bought a building for his demon hunting business. Could one person actually afford to buy a building like that, although it did fall apart rather quickly? What might be the chances of Vergil and Dante having been demon hunters during the time in-between? As the brothers were fighting Arkham in the Temen ni Gru, it was noticeable that they have fought many time together before. The way they fought seemed fluid. They didn't have to tell each other what to do. They just knew. It just came naturally, or perhaps it could be seen as a routine.

Going back to the quote now, who was "that guy" Dante was referring to? Were there more than once instance of "that guy"? Perhaps they were going to open a business together, but Vergil having left he did it on his own?

Another idea is that maybe the reason why the brothers fight well together may be due to demons who are constantly after them, because what happened to their mother might also happen to them. Then after Vergil left, Dante opened a demon hunting business on his own.

  ± Cast your soul to the sea
Why did Vergil leave? Vergil probably became craving power after his mother's death, as he sees that he was powerless against those who killed her. As he mentioned to Dante while fighting in the Temen-ni-Gru "Might controls everything, and without strength, you cannot protect anything, let alone yourself". Considering what happened to their mother, demons might also be after them as well. Having also been considered the older brother, what might have happened is that after the incident Vergil became obsessing over the idea of power to protect those who are dear to him. In other words, it might have begun as a familial obligation.

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