The three provinces which you refer to are that of Alpes Cottiae, Alpes Maritimae, and Alpes Graiae(Also referred to as Poeninae), three of the provinces which straddle the Alps in Northwestern Italy, running along the south eastern edge of France

Alpes Cottiae was originally a Kingdom controlled by Donnus, one of the rulers of the Ligurian tribes which could be found in the area around the first century BC. It was named after his son and successor Cottius, and they were integrated into the Roman Empire under Augustus and acted as Client Kings until being fully subjugated under emporer Nero. This province often acted as a safeguard for communication past the Alps for the empire.

Alpes Maritimae was founded under Augustus in 14BC after conquering the Ligurian tribes. It was established under a prefect and was used to guard coastal roads leading from France into Italy.

Alpes Poeninae was conquered around 15 BC and incorporated into the large district of Raetia. This region included a large number of Celtic tribes, so it wasn't until the reign of Emporer Claudius that the tribes were generally considered to be romanized and the region was separated. This regions border and function often changed until the rule of Diocletian when he began to reorganize the provincial system

A summary of the provincial information may be found here : Britannica