Show different scenes for different levels. Andengine

I would recommend that you use scenes instead of actions to avoid black screens between switching actions. Create your own scene manager and use it to change screens. Basic example:

public class SceneManager {
    private static Game game; // your main activity
    private static SceneManager sm;

    private Scene mScene;

    private SceneManager(){
    }

    public static void init(Game pGame){
            SceneManager.game = pGame;
    }

    public static SceneManager getManager(){
            if(game == null) throw new IllegalStateException("You must first initialize scenemanager class");
            if(sm == null) return sm = new SceneManager();

            return sm;
    }

    public void setMainMenuScreen(){
            mScene = new MainMenuScene();
            game.getEngine().setScene(mScene);
    }

    public void setGameScreen(){
            mScene = new GameScene();
            game.getEngine().setScene(mScene);
    }

    public Scene getCurrScene(){
            return mScene;
    }
}

And in your main Game.java class, you must first initialize your scene manager class and get a local instance. After that, feel free to use it according to your game logic:

private SceneManager sm;
SceneManager.init(this);
sm = SceneManager.getManager();
sm.setMainMenuScreen();

...

sm.setGameScreen();