That "telescopic" effect is achieved by maintaining your field of view, while simultaneously changing your focal length. This is called perspective distortion. You should be able to achieve a similar effect with two shots and a standard camera. An understanding of background compression would be useful here, and thankfully there was another question with a great answer for that just posted recently.
Generally speaking, this is an effect of adjusting your background compression. The concept is relatively easy to understand, however achieving it in an acceptable manner may require a fair amount of trial and error. For your first shot, you will want greater background compression, which will have the effect of bringing the background closer to you. This is achieved with a longer focal length (narrower field of view). Your second shot will want less background compression, which will have the effect of pushing the background farther away. This is achieved by doing two things with the second shot. To start, you'll need a shorter focal length (wider field of view). To keep your subject composed the same in the shot, however, you will need to get closer to your subject. The combination of a wider FOV and closer camera-to-subject distance should achieve the effect you are looking for.
You'll need to experiment a bit to get the second shot right. In particular, you'll need to pay close attention to your scenes composition. It will change in some respects (greater depth and more of the background visible), but in others it will need to remain identical. Keeping your key foreground subjects composed as identically as possible to the previous frame will take some doing. I have only mildly experimented with this effect, and never taken it to any degree of perfection, so I can't offer any tips to help here. Perhaps someone else will offer a complimentary answer that may help.
There are some basic mathematics at work for such an effect, and if your savvy enough, it might help you compose your scenes. The general formula at work is as so:
subjectDistance = widthOfScene / (2 * tan(AOV/2))
subjectDistance is the distance to subject you are trying to discern, with the given
AOV (Angle of View, or Angle @ a given Field of View). The
widthOfScene is the width of the scene being photographed, and should generally be known ahead of time. Given that formula, you could calculate the distances you would need to be from your subject with different focal lengths. Assuming you start with a 135mm portrait shot of a person with a compressed background, and want to end up with a 50mm portrait shot of a person with a decompressed background:
d_135 = 4' / (2 * tan(15/2))
d_135 = 4' / (2 * tan(7.5))
d_135 = 4' / (2 * 0.13165)
d_135 = 4' / 0.2633
d_135 = 15.2'
Start at a distance of
15' 2" @ 135mm,
d_50 = 4' / (2 * tan(39/2))
d_50 = 4' / (2 * tan(19.5))
d_50 = 4' / (2 * 0.35411)
d_50 = 4' / 0.7082
d_50 = 5.65'
End at a distance of
5' 8" @ 50mm.
You should be able to figure out the proper distance for a scene of any given width for any field of view. This is still not enough to ensure that there is very little movement of your subject in the frame between the two shots...you'll still need to work on that aspect of composition manually. Once you know the shooting distance, however, solving that problem should be considerably easier.
Angle of View Resources: