swip animatedSwitcher without a button in flutter

i have an animatedSwitcher but with effect of swip left and right, i reach that by using Two widget: a PageView builder with a transparent background and an animatedSwitcher. inside a stack i can swip smoothly between widgets.

the problem is the widgets of animatedSwitcher are scrollable but the PageView builder is above the animatedSwitcher so i cant scroll up and down widget of animatedSwitcher. (are not clickable in general).

the aim is to reach the same result as the gif down below. but without a pageview builder.

any suggestion will be helpful and thanks.

the code:

int selectedPage = 0;
  PageController _controller = PageController();

  @override
  Widget build(BuildContext context) {
    List<Widget> _pages = [
      Container(color: Colors.blue),
      Container(color: Colors.red),
    ];
    return Stack(
      alignment: Alignment.center,
      children: <Widget>[
        AnimatedSwitcher(
          duration: const Duration(milliseconds: 300),
          child: Container(
            key: ValueKey(_pages[selectedPage]),
            child: _pages[selectedPage],
          ),
        ),
        PageView.builder(
          onPageChanged: (value) {
            setState(() {
              selectedPage = value;
            });
          },
          controller: _controller,
          physics: const ClampingScrollPhysics(),
          itemCount: _pages.length,
          itemBuilder: (context, index) {
            return Container();
          },
        ),
      ],
    );
  }