Issue with ScaffoldManager and double scaffold

import 'package:flutter/material.dart';

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

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: FirstPage(),
    );
  }
}

class FirstPage extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      body: Scaffold(
        bottomNavigationBar: BottomAppBar(
          color: Colors.red,
          child: Row(
            children: [
              SizedBox(height: 45,)
            ],
          ),
        ),
        floatingActionButtonLocation: FloatingActionButtonLocation.centerDocked,
        body: Center(
          child: Column(
            mainAxisAlignment: MainAxisAlignment.center,
            children: <Widget>[
              TextButton(
                onPressed: () {
                  Navigator.push(
                    context,
                    MaterialPageRoute(
                      builder: (context) => Secondpage(),
                    ),
                  );
                },
                child: Text('change to next page'),
              )
            ],
          ),
        ),
        floatingActionButton: FloatingActionButton(
          child: Icon(Icons.add),
          onPressed: () {},
        ),
      ),
    );
  }
}

class Secondpage extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Scaffold(
      bottomNavigationBar: BottomAppBar(
        color: Colors.red,
        child: Row(
          children: [
            SizedBox(height: 45,)
          ],
        ),
      ),
      floatingActionButtonLocation: FloatingActionButtonLocation.centerDocked,
      body: Center(
        child: Column(
          mainAxisAlignment: MainAxisAlignment.center,
          children: <Widget>[
            TextButton(
              onPressed: () {
                final snackBar = SnackBar(
                  content: Text('Snackbar'),
                  behavior: SnackBarBehavior.floating,
                );
                ScaffoldMessenger.of(context).showSnackBar(snackBar);
              },
              child: Text('Display snackbar'),
            ),
            TextButton(
              onPressed: () {
                Navigator.pop(context, null);
              },
              child: Text('Back'),
            )
          ],
        ),
      ),
      floatingActionButton: FloatingActionButton(
        child: Icon(Icons.add),
        onPressed: () {},
      ),
    );
  }
}