可以通过创建绑定Service，在多个Activity之间建立永久连接。在Service中使用Binder来提供对连接的访问。具体实现步骤如下：

1. 创建一个Service并声明Binder类来提供对连接的访问。

public class MyService extends Service {
    private final IBinder mBinder = new LocalBinder();

    public class LocalBinder extends Binder {
        MyService getService() {
            return MyService.this;
        }
    }

    @Override
    public IBinder onBind(Intent intent) {
        return mBinder;
    }

    ...
}

2. 在Activity中实现ServiceConnection接口来建立和管理连接。

public class MyActivity extends Activity {
    private MyService mService;
    private boolean mBound = false;

    private ServiceConnection mConnection = new ServiceConnection() {
        @Override
        public void onServiceConnected(ComponentName className, IBinder service) {
            LocalBinder binder = (LocalBinder) service;
            mService = binder.getService();
            mBound = true;
        }

        @Override
        public void onServiceDisconnected(ComponentName arg0) {
            mBound = false;
        }
    };

    @Override
    protected void onStart() {
        super.onStart();
        Intent intent = new Intent(this, MyService.class);
        bindService(intent, mConnection, Context.BIND_AUTO_CREATE);
    }

    @Override
    protected void onStop() {
        super.onStop();
        if (mBound) {
            unbindService(mConnection);
            mBound = false;
        }
    }

    ...
}

3. 在Activity中获取Service的实例并调用其中的方法。

public void myMethod() {
    if (mBound) {
        mService.myMethod();
    }
}