Cervical swelling can be one cause of prolonged first stage.  If the swelling occurs as early as 5-6 centimeters dilation, the woman can possibly thin it out by favoring upright positions rather than prone positions.  This is because increased space in the pelvis will decrease pressure of the head on the tissues surrounding the cervix, and the circulation should improve so as to reduce the swelling.  If the swelling occurs around 8-9 centimeters dilation, it may be due to the fact that the woman has been bearing down involunarily.

According to Heart and Hands, "Squatting can increase pelvic space so dramatically that improved tissue circulation will resolve the swelling in no time" (1).

If there is a residual anterior cervical lip due to pressure of the head against the public bone.  Some suggest the application of ice, placed in the finger of a sterile glove and held against the cervix.  Once the swelling is reduced, you can attempt to push the lip back, which is also best done from the squatting position.
 

References:

(1)   Davis, Elizabeth.  (1987).  Heart and Hands:  A Midwife's Guide to Pregnancy and Birth.  2nd ed.  Berkley:  Celestial Arts, p. 95.