You don't need to manage finshing your activity, this will be managed automatically when the activity is no longer in view. Just use:
startActivity(new Intent(this, MyNextActivity.class));
And use this code in whatever method you are using to navigate the activity changes.
If you make sure your window is the background of your activities you can set the window background to a color other than black:
<item name="android:windowBackground">@drawable/window_background</item>
<shape xmlns:android="http://schemas.android.com/apk/res/android" android:shape="rectangle">
<solid android:color="@color/window_background"/>
</shape>
windowBackground in Android 6 (Marshmallow)
The other option is to manage transitions, so there is no gap between the end of the first transition and the beginning of the second. However, you have not mentioned transitions.
How to remove the delay when opening an Activity with a DrawerLayout?