Widgetの切り替えのアニメーションを作成することができます。
import 'package:flutter/material.dart';

void main() {
  runApp(const MyApp());
}

class MyApp extends StatelessWidget {
  const MyApp({Key? key}) : super(key: key);

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: 'Flutter Demo',
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: const MyHomePage(title: 'Flutter Demo Home Page'),
    );
  }
}

class MyHomePage extends StatefulWidget {
  const MyHomePage({Key? key, required this.title}) : super(key: key);

  final String title;

  @override
  State<MyHomePage> createState() => _MyHomePageState();
}

class _MyHomePageState extends State<MyHomePage> {
  int _count = 0;

  @override
  Widget build(BuildContext context) {
    return Container(
      color: Colors.white,
      child: Column(
        mainAxisAlignment: MainAxisAlignment.center,
        children: <Widget>[
          AnimatedSwitcher(
            duration: const Duration(milliseconds: 500),
            transitionBuilder: (Widget child, Animation<double> animation) {
              return ScaleTransition(scale: animation, child: child);
            },
            child: Text(
              '$_count',
              // This key causes the AnimatedSwitcher to interpret this as a "new"
              // child each time the count changes, so that it will begin its animation
              // when the count changes.
              key: ValueKey<int>(_count),
              style: Theme.of(context).textTheme.headline4,
            ),
          ),
          ElevatedButton(
            child: const Text('Increment'),
            onPressed: () {
              setState(() {
                _count += 1;
              });
            },
          ),
        ],
      ),
    );
  }
}