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[The Lord of The Rings] Gandalf vs The Balrog

Since the lotr has been re-released I had a chance to rewatch on the big screen and this scene still bothers me. The free falling scene with gandalf and the balrog ends in a huge cave with a large lake below. Fast forward to the scene with the two of them battling it out on a mountain later where gandalf strikes the final blow to defeat the balrog. How and when did this jump of location happen.
gpt
In the book it's made more clear how their fight happened.  

When they fell into the deepest depths of Moria, the Balrog was extinguished and he fled from Gandalf.  Gandalf chased him through the depths, where there are nameless monsters that are as old as the world itself.  The Balrog eventually led Gandalf to the Endless Stair - a winding stairway that goes from the deepest pits all the way to the highest peak of the Misty Mountains above Moria.  All in all, it was *eight days* between their fall from the bridge and reaching the top of the mountain.  It was a lot of stairs.

Once at the mountaintop, the Balrog was able to rekindle his flames and fight Gandalf again - it was another *three days* of battle before Gandalf was finally able to beat his enemy and cast his body down from the mountain.  And from there we know the rest - the battle was too much for Gandalf's mortal body and he died for a few weeks, before being sent back, now with even greater powers, to lead as Gandalf the White.