Based on the code you have provided, there are a couple intuitive reasons why your app would be crashing under the circumstances you have described.
Make sure you declare your third Activity in the Manifest, otherwise you will receive a null pointer exception (which could cause the app to crash) upon launching the Activity. This is a requirement for all Activities within your application. See more information here: http://developer.android.com/guide/topics/manifest/manifest-intro.html.
Also, verify that the layout for your third Activity, "activitythird", is a valid resource name and contains the TextView that you are referencing in the third activity, "textview2". If using an IDE such as Eclipse ADT or Android Studio, you should receive an indication that the resource is not found; if not automatically, at least at compile time. The same applies for the button in which initiates the launching of the third activity, "button2".