Does neutron transfer with positive Q-values enhance sub-barrier fusion cross section?

[Background] Significant enhancement of sub-barrier fusion cross sections owing to neutron rearrangement with positive $Q$-values were found for many combinations of colliding nuclei. However several experimental results on fusion reactions were reported recently in which such enhancement has not been observed in spite of a possibility for neutron rearrangement with positive $Q$-values. [Purpose] We aim to clarify much better the mechanism of neutron rearrangement in sub-barrier fusion reactions to find the other requirements (beside positive $Q$-value) which favour (or prevent) sub-barrier fusion enhancement. [Method] Channel coupling approach along with the semi-classical model for neutron transfer have been used for analysis of available experimental data. [Results] (1) Only 1n and 2n transfers with positive $Q$-values have a noticeable impact on sub-barrier fusion. Positive $Q$-value for neutron rearrangement is necessary but not sufficient requirement for additional sub-barrier fusion enhancement takes place. (2) "Rigidity" of colliding nuclei in respect of collective excitations is important that the sub-barrier fusion enhancement due to neutron rearrangement with positive $Q$-value be clearly visible. (3) Neutron binding energy in "donor" nucleus has a strong impact only in the case of fusion of light weakly bound nuclei.