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If you bring up the preview screen for your LaTeX file, you can switch to "Remote" where you can enter an arbitrary HTTP url that will be downloaded and displayed.
For example, you could save the generated PDF into Dropbox and then enter the public Dropbox URL into the remote preview address bar.
Or if your computer has a web server, you could put the PDF into a folder that is published by the web server and use that HTTP URL in Textastic's preview screen.
Just tap and hold the file in the "Files" section and choose "Open In..." in the menu that comes up. See http://www.textasticapp.com/v4/manual/lessons/How_can_I_view_an_image_file_or_open_it_in_another_app.html
Here's the documentation for the x-callback-url actions that will be supported in Textastic 4.4:
An update is currently in review at Apple. It will be available as soon as it is approved.
will be changed in the next update
Support for .scss and .sass syntax highlighting will be included in the next update.
Customer support service by UserEcho
You can refresh the file listing by using pull-to-refresh: Just pull the list down and it will update the listing.