How to modify the default transition of pages in Windows Phone 8.1?

In Windows Phone 8.1 there are 2 types of applications, Windows Phone Store Apps 8.1 and Windows Phone Silverlight 8.1.

If you are using Windows Phone Silverlight 8.1, page transitions equals 8.0 with wptoolkit:

<toolkit:TransitionService.NavigationInTransition>

and

<toolkit:TransitionService.NavigationOutTransition>

But as you're saying that you do not have the toolkit, it's probably Windows Phone Apps 8.1, so you do not have the same wptoolkit and you should use the WinRT's EntranceThemeTransition class:

<Button>
    <Button.Transitions>
        <TransitionCollection> 
            <EntranceThemeTransition/>
        </TransitionCollection>
    </Button.Transitions>
</Button> 

Reference: link