  We present a systematic study of the leading twist structure functions of the
deuteron, F_2^D, b_{1,2}^D and g_1^D in a fully relativistic approach. Our
study is based on a realistic Bethe-Salpeter amplitude for the deuteron, which
is obtained as a solution to the homogeneous Bethe-Salpeter equation with a
realistic NN kernel. Particular effort is made to connect the structure
functions to the densities of the appropriate charges and currents. This allows
for a systematic comparison between the relativistic and nonrelativistic
calculations, by analysing the same densities in both approaches. Thus, the
sources of the relativistic effects in the structure functions are understood
and clearly distinguished from variations caused by the differences in the
model parameters. We present both the formalism and extensive numerical
calculations for all steps of our analysis. We find that the nonrelativistic
and relativistic calculations are qualitatively very much alike. However, three
main features systematically distinguish a consistent relativistic approach
from the nonrelativistic one: (i) the binding effects are larger, (ii) the
effect of Fermi motion at high $x$ is stronger and (iii) the relativistic
description of the structure functions b_{1,2}^D is fully consistent, unlike
the nonrelativistic approach, which is internally inconsistent and violates the
fundamental sum rules.
