# How does a spacecraft navigate along and jump between constant v-inf lines depicted in Tisserand graphs?

Below is an example Tisserand graph showing interplanetary trajectories (in bold black).

The first one represents a trajectory from Earth till the Mercury system. In the second one, the spacecraft instead switches to the a path that increases the energy of the spacecraft upon its return to Earth from a Venus flyby (so that it can go on to Jupiter, for example).

This graph is from "Lunar and Interplanetary Trajectories" by Robin Biesbroek (Springer, 2015).

Each line represents a paths of constant v-infinity computed via Tisserand's criterion. Along a path, perihelion and period vary, but the v-inf remains constant. The graph assumes that the orbits are coplanar.

I am a bit confused regarding how this actually works out for the spacecraft:

1. What does it mean to move along a path with respect to one of the planets? I reckon that the spacecraft would naturally follow a path because at one edge of the line it is approaching the planet, and at the other end it is coming out of a flyby about that planet. If no flybys were to occur, the spacecraft would remain on a single point on the graph. Is this correct?
2. How does the spacecraft jump between lines that intersect? I understand that these lines, albeit representing different v-inf with respect to different planets, do share the same heliocentric orbital elements at the intersection point. I do not quite understand how the spacecraft changes line and goes on moving along a different line? What does the maneuver look like, qualitatively?