Some twisting movement has been detected in its neighbor the leaning Garisenda Tower, necessitating repairs or reinforcement. They have closed the piazza surrounding the two towers to facilitate the construction activity.
So if ascending the taller Torre devil Asinelli in on your list, you will have to be patient.
https://www.theguardian.com/world/2023/oct/29/bologna-seals-off-leaning-tower-fears-tilting-too-far
For me, although we love ascending steps in towers, one look at the long line waiting to climb, and the narrowness of the space, triggered my vertigo. We chose to climb the nearby clock tower (Torre dell’Orologico) instead, and it was an excellent choice. Neither claustrophobic not vertigo-inducing, and the clock mechanism is impressive.
They do have you sign a liability waiver before the last set of steps, which is more like a ship’s ladder in steepness, but it wasn’t a problem. I did turn around to descend backwards, as one would a ladder.