Let K be the set of all oriented knots up to isotopy. There are several distance functions on K, such as the Gordian distance and the ♯-Gordian distance [9]. In general, given an ‘unknotting operation’, that is, a method to untie every knot, such as the ∆-unknotting operation introduced by S. Matveev [8] (see also [10]), one can define the corresponding distance function as the minimal number o...