You can loop through the Repeater items, extract the UserControl from there  using FindControl method for you to get reference to the controls within the usercontrols.. I haven't tested on this since I'm not in my development environment but I think you can do something like below at Button Click event:

foreach (RepeaterItem item in Repeater1.Items){
       if (item.ItemType == ListItemType.AlternatingItem || item.ItemType == ListItemType.Item){
          UserControl uc = (UserControl)item.FindControl("animation1");
          if (uc != null){
             //Access the checkbox that resides within the UserControl
             CheckBox cb = (CheckBox) uc.FindControl("CheckBox1");
             if(cb.Checked){
                //Do something
             }
          }
       }
}