We test the recently proposed «Massive» Perturbation Theory (MPT) for the description of the г1p-n data at low momentum transfers. The MPT constructed on the two grounds: the first is pQCD with only one parameter added, an effective «glueball mass» mp<-Mg1<- 1 GeV; serving as an infrared «regulator»; the second stems out of the ghost-free Analytic Perturbation Theory comprising non-power perturbative expansion that makes it compatible with linear integral transformations. It is regular in the low-
energy region and could serve as a practical means for the analysis of data below 1 GeV up to the IR-limit. We study the non-perturbative Bjorken sum rule higher twists correction by using the MPT, the integral representation for infinite sum of higher twists coefficients and the QCD-inspired model for the Q2 -dependence of the generalized Gerasimov-Drell- Heam sum rule.