There is a head that receives a deadly wound by the sword and is cast into the pit. After it is cast into the pit the beast that was and was not ascends out of the pit. When did it receive it's deadly wound and when did it ascend out of the pit and become a functioning kingdom again? Be sure you don't confuse the end of the world with that head receiving a deadly wound by the sword.
Nero received a deadly wound (by himself)
Nero's death marked the end of the Julian-Claudian line of emperors. IOW, the bloodline that had received worship was "cut off".
Following the death of Nero, major catastrophes came, followed by civil wars, and attempted in revolutions in Roman provinces.
Josephus said the following about the civil wars that followed Nero's death:
“I have omitted to give an exact account of them, because they are well known by all, and they are described by a great number of Greek and Roman authors.”
The Roman historian Tacitus said the following about the time period after Nero's death"
“The history on which I am entering is that of a period rich in disasters, terrible with battles, torn by civil struggles, horrible even in peace. Four emperors failed by the sword; there were three civil wars, more foreign wars and often both at the same time"
Then came Vespasian
(Rev 13:11-12) Then I saw a second beast, coming out of the earth. It had two horns like a lamb, but it spoke like a dragon. 12 It exercised all the authority of the first beast on its behalf, and made the earth and its inhabitants worship the first beast, whose fatal wound had been healed.