  We consider the question of determining the optical drift effects in general
relativity, i.e. the rate of change of the apparent position, redshift, Jacobi
matrix, angular distance and luminosity distance of a distant object as
registered by an observer in an arbitrary spacetime. We present a fully
relativistic and covariant approach, in which the problem is reduced to a
hierarchy of ODE's solved along the line of sight. The 4-velocities and
4-accelerations of the observer and the emitter and the geometry of the
spacetime along the line of sight constitute the input data. We build on the
standard relativistic geometric optics formalism and extend it to include the
time derivatives of the observables. In the process we obtain two general,
non-perturbative relations: the first one between the gravitational lensing,
represented by the Jacobi matrix, and the apparent position drift, also called
the cosmic parallax, and the second one between the apparent position drift and
the redshift drift. The applications of the results include the theoretical
study of the drift effects of cosmological origin (so-called real-time
cosmology) in numerical or exact Universe models.
