For considering the problem of estimating different sourses of theoretical uncertainties of top-quark mass values the asymptotic structure of the perturbative QCD relation between MS bar and on-shell heavy quark masses is analysed, including the six-loop level. In the process of the studies the flavor dependence of the O(alphas^5) and O(alphas^6) corrections are estimated using three techniques, namely the effective charges motivated approach, the encoded in the asymptotic formula infrared renormalon method and the large beta0 approximation based on the explicitly known numerical values of the contributing to the coefficients of the studied relation from the leading in powers of the number of massless flavors terms. The following from the large-beta0 analysis sign-alternating structure of the expanded in powers of number of flavours estimated five- and six-loop corrections is studied. It is demonstrated that application of the first and third techniques leads to the required sign-alternation, while the second method in used by us approximation respects it only after additional imposed requirements. Uncertainties of all three used theoretical approaches are commented.