Many states have signed an interstate agreement on reciprocity but it does not necessarily waive exam, fingerprinting or additional state specific requirements. Please see details, especially the section What it is not. You MUST still apply for certification in each state that you wish to be certified to teach in.
Many states do not require that you hold NYS certification to apply in their state, only that you've completed a traditional state approved certification program plus complete their additional requirements such as exams and fingerprinting.
Some states do require that you hold certification in another state to apply for certification in their state.
It is best to check the certification website of the state you are hoping to be certified in and then check again closer to graduation as certification requirements change often.
Requirements for all states can be found easily online by searching for state name and teacher certification.
Direct link to the education departments of all fifty states and territories from the United States Department of Education.
Direct link to the certification requirements in other states from teach.org
While Relay GSE will complete out of state verification forms required by the application process for other states, it is your responsibility to research and ensure that you meet or will meet the requirements of certification in that state. The state's department of education or certification office will ultimately determine if you have satisfied the certification requirements in their state. If you have questions regarding a particular state's requirements or application process, it is best to email or speak to one of their certification representatives.