Dante's Stairway Up

Is like crossing the bridge Ponte alle Grazie then taking the steps up to San Miniato

In Purgatorio, Canto 12

He feels lighter after being purged a bit.  By off loading some P Pride he felt a sense of the incredible lightness of being and could easily climb those stairs. The seven P's signify the seven (peccatum - sins) of the seven divisions of Purgatory. He had started his climb (being a tourist) while he was still young enough to climb those stairs. 

And his climb is as easy as climbing those steps. 

The beautiful bridge is still there in Florence. 

The view of Duomo from the Rose Garden

He says: 

I drew my body up again, erect

Is like he either found himself in the astral body where you are standing looking down at your physical body lying down or

It could refers to sitting erect like in yoga. 

Today will never know another dawn

And from this point on one can climb easily

I seemed to be much more light

Delight