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I would like to have text popping in itemize

  \item<1->First item.
  \only<3->{\text{Some text.}}
  \item<2-> Second item.      

I would like to insert text (or picture) between two items continually, transiting first item upwards and lower one downwards, while bringing text in between with some entrance and exit effects (sliding from the left, from the centre...)

It seems possible to do this, judging from this question- Animate movement/transition of sections on a slide in Beamer?

However, I don't see clear answer there, could somebody make MWE for this?

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"could somebody make MWE for this?" Well, the point is that you should make a MWE. – Svend Tveskæg Mar 30 '13 at 11:40
Well @SvendMortensen I think I defined my question. It's assumed that you need to wrap the above code in \documentclass{beamer} \begin{document} \frame{...} \end{document} – Vladimir Mar 30 '13 at 12:14
@SvendMortensen On the other hand in the question related to this (link is above) someone also asked for continuous animation for entrance and exit effects, but the answer is not MWE and it's just indirectly addressing the point. I here ask for MWE which would show continuous entrance (or exit) effect for text (or figure). – Vladimir Mar 30 '13 at 12:21
Short answer is that you cannot do this in a straight-forward manner: you'll almost certainly need several pages in your PDF to create the animation by hand. The reason is that the page transitions beamer provides are a function provided by PDF viewers: all beamer does is ask for the appropriate one. In contrast, animating stuff on the page is not something that is available in the same way. It's worth noting that PowerPoint also can't create animations in PDF exports: if you make a PowerPoint with an animation, this is 'lost' when saving as PDF. – Joseph Wright Jul 31 '13 at 8:59

Here is an answer which lists out almost all transition effects available in beamer. It describes how transition works for frames.

I have tried to limit the transition to my \item and not the entire frame, but was not successful, and the transition was applied to the whole frame.

An MWE to get you started :

            \item One
            \item Two
            \item Three

Play around with the positioning of the transition effect or creating a new environment. You might get what you want.

I know there must be a better way, but I just havent discovered it.

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