Meissner effect and flux change in superconductors

[Rizke]

So I am writing a paper on superconductors, and i am trying to explain the meissner effect. However i seem to be running into conflicting information. I hoping some one can help clarify.

The effect happens, when a magnet creates a change in flux, causing a induced current in the superconductor. This current produces a induced magnetic field that is opposite from the original. this repulsiveness let the magnet float or "levitate"
But if the magnet is just resting at right before critical temperature, how is there a change in flux.

Others state, the in type II superconductor, they reach a state in between two critical fields, which trap some magnet flux lines with in. This quantum locking, locks the magnet in place.

 

[rumborak]

The first effect you describe, i.e. where an external magnetic field sets up a countercurrent in the superconductor is, to my understanding, actually not the Meissner effect. It's just a consequence of induction in a perfect conductor.
The Meissner effect on the other hand actively expels a pre-existing magnetic field when the conductor becomes superconducting. That you can't explain with plain induction, and it apparently has much more complex causes.

The Wikipedia page on the matter is pretty good, and there they point out that bringing a magnet close to a superconductor does not show the Meissner effect because it just is causing the induction effect. However, having an already close magnet start levitating after cooling down the conductor, that shows the Meissner effect.