Here's little information from Deadly Fortuna about Nero's arm
The very moment Nero devil triggered for the first time in his life (at the end of mission 5), Dante (who was in the bedroom at the top floor of Fortuna castle) felt this surge of energy through the floor that caused him to devil trigger for a split second. According to Dante, this was a reaction that he could get only from someone of the same blood origins. The novel wrote it this way: “the cry of a soul that only one of the same blood origins can detect”. He also thought that that ‘feeling’ was similar to that of Vergil, except as far as he knew he was “no longer in this world” as he put it, word for word.
Nero was supposedly dying after Agnus stabbed him in the chest at the end of mission 5. In the game, what we got is an unexplained flashback of Nero screaming Kyrie’s name. In the novel, he thought about a dream which he apparently saw a lot of lately. In the dream, there was a man he had never met staring at him. Nero described his glare as ‘cold’, but at the same time he could feel a touch of ‘gentleness’ or ‘kindness’ (the word in Japanese has two possible meanings) in him. After a moment of silence, the man (obviously Vergil) opened his mouth to ask him “Can you hear it, the cry of a soul?” And then he added, “What is your soul saying?” Instead of answering, Nero pushed the question back at him, “What’s yours saying?” Vergil smiled a little and answered, “Power… I want more power.” Hearing that, Nero replied, “I’ll take that too then.” And then Nero woke up and the devil trigger happened along with Yamato repairing itself. And the blue ghost on his back? *GASP* It’s Nero soul…!
And here's the reason why Sanctus said Nero carries Sparda's blood
In mission 11 of the game where Sanctus preached to Nero atop the Savior about how he was glad to have found someone else with Sparda’s blood (cause Dante would be a nutcase to capture), he revealed a flashback of what happened 16-17 years ago.
At that time, Santus was not the ‘Pope’ of the Order. The Pope was someone of around his age by the name Solemnis while Sanctus was a retired commander of the knights. He had thought about giving up hope of becoming Pope as the only way for a next Pope to be elected was only if the current one passed away, but in the end Sanctus was still unable to give up his dream to turn the world into what he deemed to be Paradise. In order to realize his ambitions, he had no choice but to kill Solemnis using a slow but safe method that is poison (which he abstracted from plants). It took two years for the Pope to die but no one suspected Sanctus one bit as they believed it to be natural death.
As schemed, Sanctus then became the next Pope. As part of their tradition, the new Pope was to rest in the private room at the top floor of Fortuna castle (which was believed to have been Sparda’s) in order to ‘inherit’ his ‘noble soul’, whatever that means. It was at that time when he heard someone come into the room. Sanctus was about to attack the man in defense but he paused when he could feel the clear difference in ‘strength’ through the man’s aura. The man, obviously Vergil, told him that he came only to trace Sparda’s footsteps. Based on this aura, Sanctus figured that the man wasn’t human. He wanted to ask Vergil if he was a demon or perhaps a god when he heard his guards heading for the room. Vergil went straight for the window and was about to leap out when Sanctus asked him to wait.
Vergil paused in response and looked back, only to say “I don’t mind that you pray to Sparda as a god, but do think clearly of this. One day I will surpass that god, and when that time comes, who will you worship? The one that was once god or the son who exceeded him.” (Such a badass line from Vergil) And then he disappeared through the window.
Back to present time, Sanctus told Nero this story in order to explain how he came to the conclusion that Nero was likely to be Sparda’s descendant. He was convinced that it was probably ‘that man’ from 16-17 years old that might have impregnated a woman (a prostitute to be exact) in this town and out came Nero who’s now 16-17 years old.
The End