It looks like there are a few steps to make this work:

1. Linearly interpolate the alpha of the mesh from transparent to fully opaque, or vice versa. 
* _Note 1: It seems as if the alpha starts to fade a few seconds after the effect has started._
* _Note 2: The alpha of the "effect meshes" (covered in #2 and #3) should be changed independently of the original mesh. This will help produce the desired effect._
2. Generate (just the color buffer for) a mesh with identical vertices, but make the color blue or green. The brightness of each vertice's/triangle's color should be calculated using either **random noise** (i.e. using a random number generator), or **[Perlin Noise](https://en.wikipedia.org/wiki/Perlin_noise)**; or a combination of the two. For the flashing effect, it would be best to regenerate the mesh each frame (with a different noise seed, if using Perlin Noise). Next, calculate a weighted average between the colors of this "effect mesh" and the those of the original mesh, according to how much time has passed. For instance, assuming `t` is the percentage of the way through the effect that has passed; at `t=0`, make the color buffer `0*effect_mesh + 1*original_mesh`; and at `t=0.3`, make the color buffer `0.3*effect_mesh + 0.7*original_mesh`.
3. For the vertical line effect, think about ray-tracing all the vertices (using multiple vertical rays). If a vertex is hit, make that vertex's color lighter/darker. This effect would be best done with a weighted average also, according to the time (since the lines are stronger towards the beginning).

*** Although this "Star Trek" effect varies from scene to scene, you should order these effects; don't do them all at the same time.