In this paper, we are interested in digital convexity. This notion is applied in several domains like image processing and discrete tomography. We choose to study the inflation and deflation of digital convex sets while maintaining the convexity property. Knowing that any digital convex set can be read and identified by its boundary word, we use the combinatorics on words perspective instead of a purely geometric approach. In this context, we characterize the points that can be added or removed over the digital convex sets without loosing its convexity. Some algorithms are given at the end of each section with examples on each process.