  [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.
