cupertino-page-transition-example.dart

import 'package:flutter/cupertino.dart' show CupertinoPageRoute;
import 'package:flutter/material.dart';

void main() {
  runApp(
    MaterialApp(
      home: HomePage(),
    ),
  );
}

class HomePage extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Container(
        child: Center(
          child: InkWell(
            onTap: () => Navigator.of(context).push(PageTwo.route()),
            child: Text('Clicky Here for page 2'),
          ),
        ),
      ),
    );
  }
}

class PageTwo extends StatelessWidget {
  static Route<dynamic> route() {
    return CupertinoPageRoute(
      builder: (BuildContext context) {
        return PageTwo();
      },
    );
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Container(
        child: Center(
          child: Text('Page Two'),
        ),
      ),
    );
  }
}