The purpose of this investigation is to i) give a review of the present status and conceptual evolution of height networks in America and Europe ii) redefine path independent heights on a deforming earth, iii) develop temporal corrections to be applied to present day networks, iv) investigate the potential of terrestrial geodetic techniques as a tool to detect vertical crustal movements, v) formulate a classification of mathematical models to extract and represent the vertical displacement field of the earth, vi) present a survey of changes that the geoid may experience in scale and shape, and vii) perform an actual computational example of temporal corrections to a height network in eastern Canada with temporal inhomogeneities in its levelling observations and reference surface. Recommendations are made for the redefinition of height networks regarding i) a selection of a height system ii) the mathematical formulation of the adjustment, iii) a selection of the different types of data to be used, and iv) the number and type of corrections applied to the levelling data. Several conclusions were reached: i) path independence, or holonomy, can only be achieved when both heights or height differences and reference surfaces are homogeneous in time, ii) the only rigorous approach to extract vertical crustal movements is that of a kinematic adjustment, when either scattered or connected segments are considered, iii) the temporal cross-covariance matrix of any two sets of observations plays a key role in the design and adjustment of kinematic levelling nets, iv) the geoid as a reference surface may experience changes in scale and shapes, post glacial rebound being one of the most conspicuous.
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