In this work we analyze the birefringence matrix developed for a twisted fiber in order to identify the basic optical effects that define its birefringence. The study was performed using differential Jones calculus. The resultant differential matrix showed three independent types of birefringence: circular, linear at 0 degrees and linear at 45 degrees (Jones birefringence). We applied this birefringence matrix to the description of the output state of polarization measured for three commercial fibers that due to its higher rigidity present stronger birefringence changes when twisted. The torsion applied to the erbium-doped fiber samples varied from 0 to 1440 degrees.