The Italians took control of the mountain after Battisti's death, but just like with any ground gained during the war, the Italians had great difficulty maintaining control of the mountain. Their difficulty did not just stem from the Austro-Hungarian's strength, but also because the mountain is characterized by very steep rock faces that make any sort of tactical maneuvering impossible. At this point, both sides start to dig: the mountain is gutted on the inside by the remnants of tunnels dug by both sides, trying to maneuver around the enemy by planting explosives under the enemy's position. It sounds like a tactic straight out of Spy vs. Spy, but it worked in one of the mountains, which to this day still bears the scars caused by what could only be tons of Austro-Hungarian explosives. Ironically, after a few back-and-forths, the Italians finally decisively took control of the mountain when a company of very brave young men climbed the steep rock faces of the mountain at night and ambush the small contingent protecting the mountain from above.
Nowadays, these paths and cave systems remain, and form the basis for the path going to the top of Monte Corno Cesare Battisti. These caves are great to explore, and new branches are still being found, but they are dangerous due to their relative instability and steep declines into the mountain. The steeper caves and paths along the rock faces are equipped with cable ropes, so use a via ferrata-designed harness if possible. To go up the mountain, it is not necessary to go inside the caves--but you do miss the majority of the fun. But if you do not walk inside the mountain, the paths outside are still worth it for the panoramic views around Vallarsa and Val di Pasubio it affords. As you can see from the pictures below, the hike is highly recommended during autumn.
Stairs up the mountain with steel cables, because falling would kinda suck on a beautiful day like this
Inside the caves
Tunnels lead up, down, and through the mountain
Snow on top of the Dolimiti up ahead
On top of the mountain
At the base of the mountain is Anghebeni, and next to it a former cemetery honoring the death from both sides. During the Fascist era, Mussolini ordered all WWI remains to be moved from small cemeteries like these to four ossuaries found across Vicenza: Passubio, Asiago, Monte Grappa, and Monte Cimone.