Something like this should work if you are willing to ditch the redirect. It should be a smoother transition:
$(document).ready(function(){
$("#button").click(function(){
$('#hiddenContainer').load('URL TO OTHER DOC HERE');
$(".left").animate(
{left:'50%'}, 800, 'linear'
);
$(".right").animate(
{right:'50%'}, 800, 'linear'
);
$(".top").stop(true, true).delay(800).animate(
{top:'36px'}, 800, 'easeOutBounce'
);
$(".bot").stop(true, true).delay(800).animate(
{top:'492px'}, 800, 'easeOutBounce'
);
$('SELECTOR OF YOUR OTHER CONTENT').delay(1900).fadeOut(800, function(){
$('#hiddenContainer').fadeIn(800);
});
});
});
Thats the general idea, hope it helps!