Is the Alcubierre Drive relatively free from relativistic collisions?

Related to the this question about not going SPLAT. That one was for conventional travel through space at high speeds.

Now I want to know about how things would work with an Alcubierre drive. I'm trying to understand how this will work and how it will affect other objects. I know that it is supposed to work by distorting space in front and stretching it out behind.

Now, is this little bubble of space moving with the ship inside? If so does that mean that the ship is actually stationary relative to everything inside the bubble and so isn't likely to run into anything? Does that mean the 'warping' affect pushes things aside and around the bubble? What about large objects? What size gravity wells will start to affect the ship and pull them off course?

Or does the ship move the bubble at slower speeds and matter can flow through the bubble? Would matter coming into the bubble leave time to 'maneuver' around it or would that depend on the size of the bubble?

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Is the Alcubierre Drive relatively free from relativistic collisions?

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