  Magnetic-field-induced phase transitions in the integer quantum Hall effect
are studied under the formation of paired Landau bands arising from Zeeman spin
splitting. By investigating features of modular symmetry, we showed that
modifications to the particle-hole transformation should be considered under
the coupling between the paired Landau bands. Our study indicates that such a
transformation should be modified either when the Zeeman gap is much smaller
than the cyclotron gap, or when these two gaps are comparable.
