We model the edit distance as a function in a labelling space. A labelling space is an Euclidean space where coordinates are the edit costs. Through this model, we define a class of cost. A class of cost is a region in the labelling space that all the edit costs have the same optimal labelling. Moreover, we characterise the distance value through the labelling space. This new point of view of the edit distance gives as the opportunity of defining some interesting properties that are useful for a better understanding of the edit distance. Finally, we show the usefulness of these properties through some applications.