Intrinsic regular surfaces in Carnot groups play the same role as C¹ surfaces in Euclidean spaces. As in Euclidean spaces, intrinsic regular surfaces can be locally defined in different ways: e.g., as non-critical level sets or as continuously intrinsic differentiable graphs. The equivalence of these natural definitions is the problem that we are studying. Precisely, our aim is to generalize some results proved by Ambrosio, Serra Cassano, and Vittone, valid in Heisenberg groups, to the more general setting of Carnot groups. This is joint work with Antonelli, Don, and Le Donne.