  Signatures of vertical disequilibrium have been observed across the Milky
Way's disk. These signatures manifest locally as unmixed phase-spirals in
$z$--$v_z$ space ("snails-in-phase") and globally as nonzero mean $z$ and $v_z$
which wraps around as a physical spiral across the $x$--$y$ plane
("snails-in-space"). We explore the connection between these local and global
spirals through the example of a satellite perturbing a test-particle Milky Way
(MW)-like disk. We anticipate our results to broadly apply to any vertical
perturbation.
  Using a $z$--$v_z$ asymmetry metric we demonstrate that in test-particle
simulations: (a) multiple local phase-spiral morphologies appear when stars are
binned by azimuthal action $J_\phi$, excited by a single event (in our case, a
satellite disk-crossing); (b) these distinct phase-spirals are traced back to
distinct disk locations; and (c) they are excited at distinct times. Thus,
local phase-spirals offer a global view of the MW's perturbation history from
multiple perspectives.
  Using a toy model for a Sagittarius (Sgr)-like satellite crossing the disk,
we show that the full interaction takes place on timescales comparable to
orbital periods of disk stars within $R \lesssim 10$ kpc. Hence such
perturbations have widespread influence which peaks in distinct regions of the
disk at different times.
  This leads us to examine the ongoing MW-Sgr interaction. While Sgr has not
yet crossed the disk (currently, $z_{Sgr} \approx -6$ kpc, $v_{z,Sgr} \approx
210$ km/s), we demonstrate that the peak of the impact has already passed.
Sgr's pull over the past 150 Myr creates a global $v_z$ signature with
amplitude $\propto M_{Sgr}$, which might be detectable in future spectroscopic
surveys.
