We study the galactic cosmic ray modulation in the heliosphere based on muon telescopes and ion chambers data. We analyze the modulation parameters of galactic cosmic ray transport in the heliosphere retrieved from GCR anisotropy for solar cycles 18-23 and parts of 17 and 24, covering the period 1937-2018. We find that the ratio $\alpha$ of mean free paths normal and parallel to mean interplanetary magnetic field B is polarity dependent at Earth orbit with higher values for periods around solar minima for positive polarity (A>0) than for negative (A<0). Timeline of ratio $\alpha$ for more than 7 decades, exhibits a slight ~11-year and dominant ~22-year variation and has a strongly polarity-dependent character with the considerable enhancement in the minimum epoch of solar activity for A>0 magnetic polarity. Results are confronted with current modulation theories. We examine the timeline of variance of the interplanetary magnetic field magnitude and components and their contribution in the solar cycle and solar magnetic polarity dependence of cosmic ray modulation.