  We revisit the interpretation of the cylindrically symmetric, static vacuum
Levi-Civita metric, known in either Weyl, Einstein-Rosen, or Kasner-like
coordinates. Despite the infinite axis source, we derive its Komar mass density
through a compactification and subsequent blowing up of the compactification
radius. We show that, the Komar mass density $\mu_K$ calculated in the
Einstein-Rosen frame, when employed as the metric parameter, has a number of
advantages. It eliminates double coverages of the parameter space, vanishes in
flat spacetime and when small, it corresponds to the mass density of an
infinite string. After a comprehensive analysis of the local and global
geometry, we proceed with the physical interpretation of the Levi-Civita
spacetime. First we show that the Newtonian gravitational force is attractive
and its magnitude increases monotonically with all positive ${\mu}_K$,
asymptoting to the inverse of the the proper distance in the "radial"
direction. Second, we reveal that the tidal force between nearby geodesics
(hence gravity in the Einsteinian sense) attains a maximum at $\mu_K=1/2$ and
then decreases asymptotically to zero. Hence, from a physical point of view the
Komar mass density of the Levi-Civita spacetime encompasses two contributions:
Newtonian gravity and acceleration effects. An increase in $\mu_K$ strengthens
Newtonian gravity but also drags the field lines increasingly parallel,
eventually transforming Newtonian gravity through the equivalence principle
into a pure acceleration field and the Levi-Civita spacetime into a flat
Rindler-like spacetime. In a geometric picture the increase of $\mu_K$ from
zero to $\infty$ deforms the planar sections of the spacetime into ever
deepening funnels, eventually degenerating into cylindrical topology.
