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General covariance is tested controversial after the investigations on gravitational redshift and acceleration. Further inspections on differential geometry indicate the opportunities of inequality of mixed derivatives of bases for the transformations between Riemannian spaces that will then lead to failure of the classical equations of Christoffel symbols, that is the main reason that causes controversies on general covariance. In fact, Christoffel symbols and base derivatives are both valid methodologies for analysis in gravitational fields. Measurable experiments on gravitational redshifts and accelerations have been sponsored to support the theoretical results. Conclusions have been drawn that light speed keeps general covariance in gravitational fields, but light energy momentum would not, while massive matters in gravitational fields do not travel in general covariance. Consequently, inferences on kinematics and relativistic release were put into research, which have got surprising verifications in applications. The problems in classical equations of light ray deflection, time delay of radar echoes and motion of massive matters have been revisited in details, which would help to kick off the errors and help us to find out real kinematics. Relativistic releases reveal the mechanism of evolutions of active galactic nuclei. Relativistic emissions and relativistic absorptions with giant redshifts would have involved with fantastic mystery of intrinsic structures of matters that we know less. Theoretical researches, experimental and observational verifications may continue to bring about comprehensive supports to the conclusions and inferences.